Classifying Bitcoin’s Safe Haven Role Using Explainable AI: Evidence from US Macroeconomic Stress Episodes

Classifying Bitcoin’s Safe Haven Role Using Explainable AI: Evidence from US Macroeconomic Stress Episodes | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Classifying Bitcoin’s Safe Haven Role Using Explainable AI: Evidence from US Macroeconomic Stress Episodes Manjunath B R This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6909016/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 25 Oct, 2025 Read the published version in Quality & Quantity → Version 1 posted You are reading this latest preprint version Abstract This study examines the role of Bitcoin as a potential safe haven during periods of macroeconomic stress caused by US policy shocks. Utilizing daily data from January 2020 to March 2025, including Bitcoin, Gold, the S&P 500, VIX, CPI, and the Federal Funds Rate, we create an innovative divergence-based framework. Bitcoin qualifies as a safe haven only when it appreciates while both Gold and the S&P 500 decline, reflecting flight-to-safety behavior. An XGBoost classifier, trained on engineered divergence and macro-financial features, significantly outperforms Random Forest and Logistic Regression, achieving an AUC of 0.997 and a recall rate of 0.88. SHAP-based explainability indicates that Bitcoin’s return divergence from traditional assets is the most significant predictor of its safe-haven behavior. The results confirm that Bitcoin does not consistently act as a hedge but exhibits episodic, stress-driven, safe-haven characteristics. This framework enhances the understanding of Bitcoin’s behavior in response to systemic shocks, providing transparent, data-driven decision support for investors facing financial uncertainty. Divergence modeling Explainable AI Logistic Regression XGBoost SHAP Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 Figure 18 Figure 19 1. Introduction In the face of increasing macroeconomic uncertainty, characterized by inflationary shocks, aggressive monetary tightening, and global crises such as the COVID-19 pandemic, investors are turning to resilient assets that protect their capital during downturns in traditional markets. Traditionally, safe-haven assets such as Gold and sovereign bonds have provided this downside protection. A safe haven, as described by Baur and Lucey ( 2010 ), refers to an asset that is either uncorrelated or negatively correlated with a risk asset during periods of severe market stress. While the traditional understanding of safe haven behavior relies on these uncorrelated or negatively correlated responses in times of systemic stress, we adopt a divergence-based labeling approach, designating Bitcoin as a conditional safe haven exclusively when its value appreciates. At the same time, both Gold and the S&P 500 fall, as this shows a clear and observable trend in investor behavior, with funds shifting away from traditional hedges and high-risk options. The potential for Bitcoin to act as a conditional safe haven, particularly during periods of US economic and policy-driven turmoil, has garnered attention due to its decentralized nature, limited supply, and algorithmic creation (Shahzad et al., 2019 ; Umar et al., 2021 ). This study focuses on the timeframe from January 2020 to March 2025, a period characterized by significant changes in US policy. These changes include the COVID-19 market crash, post-pandemic inflation, and the Federal Reserve’s stringent interest rate hikes. Importantly, our analysis encompasses not only financial crashes but also recurrent instances of macroeconomic volatility driven by policy, such as unexpected inflation, interest rate fluctuations, and tapering announcements, as observed by Choi et al. ( 2022 ). These factors have been recognized as critical sources of stress in today’s financial markets. Bitcoin’s appeal theoretically lies in its resistance to inflation and decentralization; however, the evidence remains ambiguous. Early studies (Dyhrberg, 2016a ) identified hedging traits similar to those found in Gold and traditional currencies. However, subsequent research has shown that Bitcoin exhibits pronounced volatility, susceptibility to contagion, and a positive correlation with stocks during market crises (Griffin & Shams, 2020 ). These fluctuations suggest that Bitcoin’s status as a safe haven is neither stable nor reliable; it tends to emerge only under specific macro-financial conditions influenced by liquidity shocks, policy uncertainties, and investor sentiment (Yae & Tian, 2024 ; Cheng & Yen, 2020 ). Moreover, Bitcoin’s high volatility challenges its image as a typical safe haven, especially when compared to stable government bonds or traditional currencies. However, its relevance is still possible in certain divergence instances. Numerous advanced econometric models, including wavelet decompositions, quantile regressions, and co-explosivity models (Bouri et al., 2019 ), have explored these interaction effects. However, they often struggle to effectively model the nonlinear and adaptive relationships that are present in volatile assets, such as cryptocurrencies. Consequently, more studies are turning to deep learning and AI methods, as these approaches are better equipped to handle chaotic financial time series (Fawaz et al., 2019 ; Lahmiri & Bekiros, 2019 ). Architectures such as Long Short-Term Memory (LSTM) and Convolutional Neural Network (CNN) have significantly improved Bitcoin price forecasting (Li & Dai, 2020 ; Livieris et al., 2021 ; Ji et al., 2019 ). Nonetheless, there is limited research on these technologies within macro-integrated classification systems that aim to evaluate Bitcoin as a safe-haven asset. The integration of macroeconomic indicators, such as the Consumer Price Index (CPI) and the Fed Funds Rate, along with sentiment measures like the Volatility Index (VIX), into AI models to analyze behavioral responses to U.S. policy shocks has been rarely examined (Shen et al., 2021 ; Paule-Vianez et al., 2020 ). Recent improvements in this field (Bianchi et al., 2021; Lee, 2024 ) have enhanced forecasting precision by utilizing attention-based additive methods and hybrid deep learning frameworks, thereby providing more accurate explanations for volatility in predictive trading models. These advancements indicate a transition from simple machine learning to more interpretable and reliable decision-making models. Many recent studies prioritize correlation metrics while overlooking the advantages of explainable machine learning classifiers. These classifiers can leverage probabilistic divergence behavior instead of merely tracking coincident movements (Šestanović & Kalinić Milićević, 2023 ; Kim et al., 2016 ). A divergence-style framework, such as when Bitcoin rises while Gold and stocks decline, illustrates shifts in investor preferences away from traditional stores of value, including assets perceived as safe havens against extreme risks, like equity and commodities. This viewpoint facilitates a deeper understanding of genuine capital substitution and enables a systematic classification that exceeds simple correlation. The lack of interpretability significantly hampers its applicability in policy-making and institutional risk management. SHapley Additive exPlanations (SHAP) is increasingly recognized as the key standard for interpretability, enabling regulatory bodies to monitor models that influence decision-making across all areas of financial services (Kumar & Mittal, 2022; Zhang & Li, 2023). Recent applications have demonstrated the effectiveness of SHAP in uncovering and quantifying nonlinear relationships among asset returns, volatility, and policy shifts, thereby enhancing the necessary transparency for robust decision-making in critical financial sectors (Lundberg & Lee, 2017 ). Its expanding use is forging a connection for AI predictions, where economic principles still hold, and investor behavior can be clarified during times of uncertainty. To empirically validate this divergence theory, we are establishing a supervised learning classification framework that utilizes macro-sensitive features and interpretable AI to identify safe haven episodes and their key drivers. This paper makes five key contributions : It proposes a framework for divergence-based labeling that recognizes Bitcoin as a conditional safe haven when it rises, while both Gold and the S&P 500 decline, signaling capital flight from conventional markets. It creates macro-informed features that utilize rolling volatility, lagged macroeconomic signals, and return divergence ratios to reflect market stress and changes in behavior across different policy regimes. It implements and benchmarks XGBoost, a robust ensemble model, against random forest and logistic regression classifiers. It employs SHAP to rank and elucidate the factors influencing safe haven predictions, underscoring the importance of explainability in economic and policy contexts. It introduces a prescriptive probability banding system that allows risk managers to interpret model outputs (e.g., high-certainty versus low-certainty safe haven events) for real-time asset allocation. Together, these contributions form a new, transparent, and actionable framework that links financial theory, interpretable AI, and macroeconomic factors, emphasizing Bitcoin’s potential status in portfolios during periods of crisis amid policy uncertainty. While we focus on the Gold as a traditional benchmark, it is essential to note that US Treasuries are often regarded as the quintessential safe-haven asset, especially during times of systemic crises and policy shocks (Baur & Lucey, 2010 ; Baur & McDermott, 2010 ). Due to variations in liquidity profiles, yield dynamics, and market behavior, US Treasuries were excluded from our divergence-based operational framework. However, we recognize this as a significant limitation and suggest its incorporation as a beneficial extension for future research. 2. Literature Review 2.1 Bitcoin as a Safe Haven: A Mixed Narrative Baur and Lucey ( 2010 ) define a safe haven as an asset that maintains or appreciates during severe market stress. This differs from a hedge, which is effective in normal market conditions, and a diversifier, which only slightly mitigates risk. Understanding this distinction is crucial, as many studies mix these terms, resulting in unclear interpretations of Bitcoin’s function. Recent research has explored Bitcoin’s role as a safe-haven asset, producing mixed results. For instance, Liu & Yuan ( 2024 ) reassessed the crypto safe-haven hypothesis by analyzing Bitcoin against both fiat currencies and Treasuries during periods of monetary tightening, uncovering behaviors influenced by volatility clustering and investor flows. Bouri et al. ( 2017 ) and Dyhrberg ( 2016b ) were early proponents of the idea that Bitcoin exhibits partial hedging behavior; however, this behavior is affected by structural breaks and volatility clustering. In a similar vein, Shahzad et al. ( 2019 ) employed dynamic copula and Markov-switching techniques to uncover regime-specific dependence structures between Bitcoin and traditional safe-haven assets. However, much of the existing safe haven literature focuses on US government bonds, mainly Treasuries, as the standard asset during episodes of global financial stress. Baur and McDermott ( 2010 ), among others, note that Treasuries exhibit a steady inverse correlation with equities and high liquidity in crises. Our decision to exclude US Treasuries from our modeling approach results from our emphasis on high-frequency divergence signals involving crypto and commodity assets, and we recognize this as a structural limitation of our analytical reach. Umar et al. ( 2021 ) investigated Bitcoin’s hedge functionality using wavelet quantile-on-quantile analysis, incorporating the US Partisan Conflict Index (PCI) and Economic Policy Uncertainty (EPU). Their findings indicate that Bitcoin’s safe-haven characteristics were quantile-specific, asymmetric, and varied over time, with evidence of bidirectional feedback during economic stress events, such as elections and the COVID-19 pandemic. Yae and Tian ( 2024 ) introduced a novel method for analyzing upward price momentum in Bitcoin. They observed a decoupling of equities, which they linked to passive institutional rebalancing. The authors discovered that a 0.1 drop in the correlation between Bitcoin and the S&P 500 forecasted a 1.5% chance of a positive return the following day. They emphasized that this trend did not hold for Gold or treasuries. 2.2 Machine Learning and Deep Learning in Crypto Forecasting Most conventional econometric methods (such as GARCH and VAR) struggle to fully capture Bitcoin’s distinct nonlinearities, long memory, and structural breaks. This limitation creates opportunities for advanced learning models to develop. Li and Dai ( 2020 ) proposed a hybrid model that merges convolutional neural networks with long short-term memory (CNN-LSTM) and incorporates macro-financial and sentiment indicators like the S&P 500, oil prices, Baidu Index, and Fed Funds Rate. The CNN-LSTM hybrid model outperformed standalone CNN, LSTM, and ANN methods, as well as those focused solely on short-term predictions. These findings demonstrate that the combination of convolutional pattern recognition and LSTM enhances the analysis of temporal sequences. Šestanović and Kalinić Milićević ( 2025 ) performed a regime-aware analysis utilizing the Bai–Perron methodology to categorize markets into bullish, bearish, and volatility regimes. Their integrated feature framework, comprising tweets, VIX, S&P 500, and Google Trends, reveals that CNNs are most effective during downturns, LSTMs thrive in uptrends, and FFNNs excel in volatile conditions. Jang and Lee ( 2018 ) introduced a Bayesian Neural Network (BNN) method to forecast Bitcoin prices. This technique integrates blockchain metrics, such as hash rate and transaction volumes, with macroeconomic indicators. They evaluated this methodology in real time, utilizing walk-forward validation, which steadily advances over time to yield precise predictions. Their approach surpassed both SVR and linear models. While its primary focus is price forecasting, it also provides a solid framework for safe-haven classification. Abdalhammed et al. ( 2022 ) analyzed the Vanilla LSTM model in an uncertain environment that restricted the use of historical data, confirming the model’s robustness when dealing with limited datasets. They also incorporated GARCH solutions, connecting their model’s application to market efficiency. In a similar vein, Atsalakis et al. ( 2019 ) utilized PATSOS, a closed-loop neuro-fuzzy system that combines an adaptive neuro-fuzzy inference system (ANFIS) with an artificial neural network, achieving a hit rate of 63.22% and delivering returns 71% above the buy-and-hold strategy. This accomplishment represents a significant advancement, showcasing clarity and factuality about its comprehensiveness while exploring new methods for effectively integrating measures and data in response to news events.s 2.3 Divergence Logic and Risk Prediction The literature frequently discusses inter-asset divergence, which refers to the phenomenon where asset classes move in opposite directions, to help understand capital reallocation across different markets. Bouri et al. ( 2020a ) and Guesmi et al. ( 2019 ) noted that such a divergence pattern indicates a risk-off market. The model proposed in this research supports the notion of Bitcoin as a safe haven, with rising Bitcoin prices accompanied by falling Gold and S&P 500 values, which strengthens this assertion. Additionally, Li and Dai ( 2020 ) demonstrated that external macroeconomic factors, such as the Fed Funds rate, oil prices, and equity returns, play a significant role in enhancing the accuracy of forecasting the dependent variable. By incorporating volatility indicators from the derived values (such as rolling standard deviations) and ratios of divergences, we can create a more detailed and conditional feature set for analysis. 2.4 Explainable AI and SHAP: Enhancing Financial Model Transparency As neural networks evolve, the issue of transparency becomes increasingly crucial. Recently, SHAP (Lundberg & Lee, 2017 ) has emerged as the foremost technique for interpreting AI models in the finance industry. In their empirical study, Šestanović and Kalinić Milićević ( 2023 ) demonstrated how SHAP can inform the development of price predictions and highlighted the significant impact of sentiment and non-economic volatility on forecasts derived from neural networks. Nevertheless, SHAP remains underutilized in classification models for crypto risk modeling, such as divergence-based safe-haven forecasting. Additionally, SHAP guarantees variation in feature attribution, along with local consistency and local accuracy (Lundberg & Lee, 2017 ), setting it apart from competing feature attribution methods. This includes documenting the importance of features like the VIX, divergence, and lagged volatility through SHAP classification. This methodological framework helps to address the existing gap by improving transparency in crypto finance while meeting regulatory disclosure obligations. Recent studies, such as those by Baklanova et al. ( 2023 ), Shaikh (2024), and Todorovska et al. ( 2023 ), employ SHAP to identify factors influencing the cryptocurrency market. These researchers explain their models through weights associated with economic events, including liquidity constraints, news sentiment, and macro spillovers. The factors highlighted in these studies are expected to further the application of SHAP in asset classification and influence investors’ risk perceptions. 2.5 Gaps and Our Contribution: Despite notable progress in cryptocurrency research, four main gaps remain in understanding Bitcoin’s role as a conditional safe haven: Inadequate classification frameworks relying on macro indicators : Numerous earlier studies (Bouri et al., 2017 ; Shahzad et al., 2019 ) focus on correlation, tail dependence, or wavelet decompositions; however, they largely overlook rule-based, ex-ante frameworks that integrate macroeconomic indicators (CPI, Fed Funds Rate) and market sentiment (VIX). Emphasize price predictions over risk-role classifications : Numerous earlier studies, such as those by Ji et al. ( 2019 ) and Livieris et al. ( 2021 ), have focused on forecasting Bitcoin prices but have neglected its role as a conditional hedge during periods of systemic macro-financial stress. Emphasizing price prediction over risk-role classification : Earlier studies have focused on forecasting Bitcoin prices (e.g., Ji et al., 2019 ; Livieris et al., 2021 ) without categorizing its behavior as a conditional hedge during periods of systemic macro-financial stress. Lack of divergence-driven safe haven reasoning : Limited research investigates Bitcoin’s ascent while Gold and equities decline, overlooking capital flight trends observed in times of crisis. Insufficient integration of explainable AI (XAI) : Although ML models are utilized in crypto forecasting (e.g., Li & Dai, 2020 ), few studies implement SHAP or similar XAI methods to clarify the factors influencing predictions, which compromises transparency for institutional adoption. This study makes five significant contributions to the literature: Macro-Informed Divergence Logic : We propose a rule-based framework that is sensitive to macroeconomic conditions, classifying Bitcoin as a conditional safe haven when its value increases, while Gold and the S&P 500 experience concurrent drawdowns. Comprehensive Feature Engineering : Our dataset encompasses divergence metrics, macroeconomic indicators (such as the CPI and Fed Funds), and market sentiment (as measured by the VIX), reflecting economic stress and investor uncertainty in response to US policy shocks. Effective Supervised Learning Models : We evaluate and compare XGBoost with Random Forest and Logistic Regression to identify safe-haven events, showing better results in both recall and AUC. SHAP-based Interpretability : We utilize SHAP to reveal both global and local feature contributions, thereby enhancing model transparency and facilitating a connection between predictions and economic behavior. Prescriptive Confidence Stratification : We present a probabilistic decision support system that organizes predictions into actionable levels of safe-haven confidence, providing practical utility for institutional investors. Although the study examines divergence from the Gold and S&P 500 indices, it does not account for US Treasuries, which are commonly viewed as benchmark safe-haven assets. This omission is acknowledged as a limitation and presents a valuable opportunity for future research to extend the divergence-based classification to fixed-income instruments. Together, these insights connect theory, machine learning, and explainable AI to present a new, transparent method for understanding Bitcoin’s fluctuating characteristics as a safe haven. The logic of divergence is based on the capital substitution theory. As conventional assets decline and Bitcoin rises, it suggests a potential shift towards digital alternatives during times of systemic turmoil. 3. Research Methodology 3.1 Data Acquisition and Preprocessing This research utilizes daily financial and macroeconomic data spanning from January 1, 2020, to March 31, 2025. This timeframe encompasses various global shocks, such as the COVID-19 pandemic, spikes in inflation, and shifts in policy rates. The daily frequency was chosen to capture the more nuanced divergence dynamics of Bitcoin compared to traditional safe-haven assets during periods of heightened turmoil. The selected sample period incorporates several systemic macro-financial shocks that influenced investor behavior, market volatility, and asset allocation. These shocks consist of: The onset of the COVID-19 crisis and the swift global fiscal and monetary measures taken in early 2020 (Bouri et al., 2020b ). The ongoing rise in inflation and disruptions in supply chains throughout 2021 and 2022 (Cleveland Federal Reserve Bank, 2023 ). The Federal Reserve’s steep interest rate increases and quantitative tightening policies started in March 2022 (Board of Governors of the Federal Reserve System, 2022a , 2022b ). Continual geopolitical and policy uncertainties, which encompass stagflation risks and fluctuations in the US debt ceiling during 2024–2025 (Congressional Research Service, 2024 ). These events led to repeated macro-policy stress regimes, making this timeframe an ideal time to analyze Bitcoin’s conditional safe-haven behavior during US policy-induced shocks. The variables and sources utilized are as follows: Data for mid-market Bitcoin prices (BTC/USD), daily closing gold prices (XAU/USD), and the S&P 500 Index (SPX) is sourced from the Refinitiv Datastream platform, known for offering high-quality financial data series. The CBOE Volatility Index (VIX) was obtained from Refinitiv to assess daily investor sentiment and systemic risk. In this context, macroeconomic indicators include the Consumer Price Index (CPI) (CPIAUCSL) and the Federal Funds Effective Rate (FedFunds), both derived from Federal Reserve Economic Data (FRED). As CPI and FedFunds are available monthly, both metrics were forward-filled to align with the daily granularity of the market data. This adhered to the established guidelines for mixed-frequency data (Aljinović et al., 2022 ). This method preserves the temporal integrity of the modeling process and avoids potential leakage that could result in misleading correlations. To ensure variance stability and enhance comparability among asset classes, all raw price series were converted into logarithmic returns through the following transformation (using Eq. 1): \(\:{r}_{t}=\text{ln}\left(\frac{{P}_{t}}{{P}_{t-1}}\right)\) -------(1) Where r t is the log return of the asset on day t , P t represents the closing price of the asset at times t and t-1 . This adjustment stabilizes variance and makes returns approximately stationary. This method stabilizes variance and offers insights into percentage changes (Gandal et al., 2018 ). To test for stationarity in the transformed series, the Augmented Dickey-Fuller (ADF) test was conducted, confirming the suitability of using return-based features for time series classification (Šestanović & Kalinić Milićević, 2025 ). There were no missing or incomplete values to impute from this dataset. 3.2 Binary Target Construction: Safe Haven Flag A novel binary classification target Y t ∈{0,1} was engineered to reflect the safe haven behavior of Bitcoin (using Eq. 2)as follows: \(\:{Y}_{t}\:=\:\left\{\begin{array}{c}1\\\:0\end{array}\right.\:\begin{array}{c}if\:{r}_{t}^{BTC}\:>\:0\:\wedge\:\:{r}_{t}^{Gold\:}\:<\:0\:\wedge\:\:{r}_{t}^{SPX}\:<\:0\\\:Otherwise\end{array}\) ------- (2) This illustrates instances where Bitcoin’s returns rise, even as those of Gold and the S&P 500 decline or exhibit positive returns. This finding is consistent with the safe haven definitions based on divergence, as discussed in the literature (Paule-Vianez et al., 2020 ; Shahzad et al., 2019 ). The flag relies exclusively on daily-return data at time t , incorporating the asset prices at t and t-1 . This approach ensures that the target label can be observed beforehand, independent of subsequent information, thus facilitating the acceptance of causal relationships within real-time classification systems. In this context, while we adopt a risk-off posture, it should not be considered "hedging" in the correlation sense (Baur & Lucey, 2010 ); instead, it frames our conditional flight-to-safety behavior within a rule-based structure. Although this divergence flag may indicate some short-term hedging activity, it ultimately hinges on the set threshold limit for the flag. A threshold-based flag provides a clear, reproducible, and easily interpretable signal in real time, reinforcing the idea that expectations represent the most effective way to showcase Bitcoin’s substitutive role during a downturn in an asset class. 3.3 Feature Engineering We developed a formal list of characteristics, including inter-asset return differentials and macroeconomic indicators, to accurately model Bitcoin’s behavior as a potential safe haven during periods of divergence. 3.3.1 Divergence Indicators: The key defining variables are formulated as pair-wise return differentials between Bitcoin and traditional assets (using Eq. 3): \(\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{Div}_{BTC\:\:-\:Gold,t\:}=\:{r}_{t}^{BTC}\:-\:{r}_{t}^{Gold},\:\:\:\:\:\:{Div}_{BTC\:-\:SPX,t\:}=\:{r}_{t}^{BTC}\:-\:{r}_{t}^{SPX}\) -------(3) These divergence measures consider directional discrepancies in asset returns and employ substitution theory within capital portfolios. Investors allocate funds across assets with varying risk profiles, utilizing substitution theory especially during volatile times. Additionally, previous studies indicate that hedging strategies and transitions to safer assets tend to happen when gold and equities face negative returns at the same time, serving as "traditional hedge" assets (Shahzad et al., 2019 ; Paule-Vianez et al., 2020 ). 3.3.2 Lagged Macro Signals : To include pertinent macro-financial context, the following lagged indicators were added (using Eq. 4): \(\:{CPI}_{t-1},\:{VIX}_{t-1},\:{FedFunds}_{t-1}\) -------(4) Lagging offers models certainty that they rely exclusively on information available at decision time t , eliminating forward-looking bias. These elements are linked to inflationary pressures, market volatility, and the position of monetary policy, affecting asset substitution and the appeal of safe havens. 3.3.3 Data Transformation and Normalization To mitigate the impact of extreme return values, the features were winsorized according to the 95th percentile rule (Fawaz et al., 2019 ). This approach improved the original feature structure while simultaneously minimizing potential outliers and extreme returns. Subsequently, all relevant features were MinMax normalized (Li & Dai, 2020 ), a crucial step for dimensionality reduction and ensuring compatibility with models that rely on gradient descent algorithms, such as XGBoost. These engineered features serve as a solid and economically interpretable basis for classifying safe haven behavior. 3.3.4 Why Machine Learning Models? Most studies on safe haven assets mainly employed econometric models, including GARCH family models, Markov-switching models, quantile regressions, and threshold regressions (Bouri et al, 2017 ; Shahzad et al, 2019 ). Although these econometric models provide valuable insights, they frequently encounter limitations arising from assumptions about stationarity, linearity, and their limited features. In contrast, machine learning algorithms such as XGBoost and Random Forest: Identify nonlinear connections and interactions among engineered features, including divergence ratios, rolling volatilities, and macro lags. Manage imbalanced datasets more efficiently. Facilitate real-time classification with scalability. Most importantly, it provides explainability through SHAP, offering actionable insights for financial decision-making. Therefore, ML provides predictive capabilities and transparency, addressing the shortcomings of conventional methods. 3.4 Modeling Approaches We analyzed Bitcoin’s safe haven properties through three supervised learning techniques: Logistic Regression, Random Forest, and Extreme Gradient Boosting (XGBoost). Each of these methods has distinct advantages in terms of interpretability, handling nonlinearity, and optimization. Ultimately, we selected XGBoost for its ability to efficiently model ‘tabular data’ with diverse feature types, its capability to identify nonlinear interactions, and its lower need for strict parameter selection. This makes it more resilient to issues like multicollinearity and class imbalance, which frequently occur in financial time series. In contrast to threshold models like Markov switching or quantile regression that require users to specify regimes and can be unstable with high noise, XGBoost adeptly adapts to structural changes and fluctuations over time. Furthermore, the performance benefits of applying XGBoost in finance have been thoroughly documented (Ji et al., 2019 ; Umar et al., 2021 ). 3.4.1 Logistic Regression (LR) - interpretable baseline: \(\:\text{l}\text{o}\text{g}\left(\frac{P\left({Y}_{t}=1\right)}{1-P\left({Y}_{t}=1\right)}\right)={{\beta\:}}_{0}+{\sum\:}_{i=1}^{k}{{\beta\:}}_{i}{X}_{i,t}\) -------(5) Logistic regression (Eq. 5) provides a straightforward and effective baseline, allowing for clear interpretation of coefficients and accurate comparisons with more complex models (Bouri et al., 2019 ). 3.4.2 Random Forest (RF) – an ensemble of de-correlated decision trees: \(\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\widehat{{Y}_{t}}=\text{mode}\left\{{T}_{1}\left({X}_{t}\right),{T}_{2}\left({X}_{t}\right),\dots\:,{T}_{B}\left({X}_{t}\right)\right\}\) -------(6) Random Forests (as detailed in Eq. 6) capture nonlinear relationships among variables by employing bootstrap aggregation and introducing random feature variation. This approach results in robust models that mitigate the risk of overfitting (Šestanović & Kalinić Milićević, 2023 ). 3.4.3 Extreme Gradient Boosting (XGBoost) – optimized additive model: \(\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{\mathcal{L}}^{\left(\mathcal{t}\right)}={\sum\:}_{i=1}^{n}l\left({y}_{i},{\widehat{y}}_{i}^{\left(t-1\right)}+{f}_{t}\left({x}_{i}\right)\right)+{\Omega\:}\left({f}_{t}\right)\) -------(7) where fₜ(x i ) represents the tree introduced in iteration t , and Ω serves to regularize complexity. XGBoost (using Eq. 7) demonstrates strong performance on structured datasets and exhibits resilience against class imbalance (Ji et al., 2019 ; Li & Dai, 2020 ). To address the skewed safe haven, class weighting was incorporated into model training to mitigate bias toward the majority class (Umar et al., 2021 ). All models were developed in Python with scikit-learn , xgboost , and shap for modeling and explainability. The benchmark model employed Logistic Regression, while Random Forest was chosen to capture nonlinear relationships. XGBoost was utilized for its scalability and firm performance in financial classification tasks. 3.5 Model Interpretability using SHAP In order to achieve transparent AI and encourage economic explanation, we adopted(using Eq. 8) SHAP (SHapley Additive explanations) to measure feature contributions globally and locally. The SHAP explanation model is defined as: \(\:f\left(x\right)={{\upvarphi\:}}_{0}+{\sum\:}_{i=1}^{M}{{\upvarphi\:}}_{i}\) -------(8) Where ϕ 0 is the model’s expected output, and ϕ i denotes the marginal contribution of feature i to the prediction, for instance, x . SHAP values fulfill essential interpretability properties, including local accuracy, consistency, and robustness to missingness. To assess the overall significance of features, global SHAP values were determined by averaging the absolute SHAP values from the test set. This method ensures that the model’s interpretation aligns with its performance on unseen data, rather than merely mirroring its behavior during training. SHAP Summary Plots revealed that the divergence indicators between Bitcoin-Gold and Bitcoin-SPX were the strongest influencers of the model’s predictions. SHAP Force Plots provided explanations tailored to individual instances for the safe haven designations observed during market stress situations. The use of SHAP significantly enhances explainable AI (XAI) in the context of modeling high-stakes financial markets, boosting overall interpretability and clarity in decision-making. In addition to providing model explainability, SHAP offers prescriptive decision support. For example, by highlighting divergence spreads or macroeconomic factors, institutional analysts can pinpoint which signals are most influential in safe-haven behavior during times of stress. A notable SHAP value for the bitcoin–SPX 500 divergence ratio, for instance, would support increasing crypto exposure in risk-off situations. This importantly links AI-derived insights with actionable investment strategies. 3.6 Model Evaluation Metrics To evaluate performance in line with actual market conditions, we implemented an 80/20 stratified train-test split to preserve the relative class distribution of the binary safe haven flag (Yₜ ∈ {0, 1}). Given that financial time series exhibit non-stationarity and dependencies, we chose the 80/20 stratified train-test split over k-fold cross-validation . Using k-fold cross-validation could lead to parameters that inaccurately estimate performance or skew performance metrics due to data pooling across folds, especially with an imbalanced dataset. The evaluation of model performance utilized the following standard classification metrics: Accuracy Precision Recall F1 Score Receiver Operating Characteristic Area Under the Curve (ROC-AUC) These are defined as \(\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\text{Accuracy}=\frac{TP+TN}{TP+TN+FP+FN}\) -------(9) \(\:\text{Precision}=\frac{TP}{TP+FP}\) -------(10) \(\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\text{Recall}=\frac{TP}{TP+FN}\) -------(11) ROC - AUC = Area under the Receiver Operating Characteristic curve -------(13) These performance metrics offer a comprehensive view of model efficacy, particularly when class imbalance can obscure accuracy (Shahzad et al., 2019 ; Umar et al., 2021 ). The F1 score effectively balances false positives against false negatives, whereas the ROC-AUC highlights the model’s proficiency in distinguishing between thresholds. 3.7 Model Validation Results and Theoretical Significance Our framework evaluates both statistical accuracy and the model’s capacity to accurately identify divergence related to safe haven events, as outlined in Section 2.1 . In this regard, recall is especially vital. If a model fails to recognize a genuine safe haven event, it may result in suboptimal capital allocation decisions amid macro-policy stress. Likewise, precision is essential to avoid issuing false safety signals. XGBoost excelled in F1 and AUC metrics compared to logistic regression and random forest across all models, demonstrating its strong robustness and effectiveness in capturing the nonlinear, conditional aspects of Bitcoin’s safe-haven properties. This method of classification and evaluation directs our focus towards the idea that divergence-based patterns, informed by macro factors, can be systematically and transparently modeled to highlight Bitcoin’s sporadic but significant role as a safe haven. 4. Results and Discussions 4.1.1 Descriptive Statistics This study analyzes daily data from January 1, 2020, to March 31, 2025, encompassing 1,876 observations across three major asset classes: Bitcoin, Gold, and the S&P 500. In addition to core asset returns, we incorporated various macroeconomic indicators, including the VIX Index, CPI, and the FED FUNDS rate. Furthermore, we developed several features focusing on factors such as directional return divergence, relative strength, and lagged macroeconomic conditions that affect safe-haven attributes. To assess safe-haven behavior systematically, we created a binary classification rule: A day is designated as a safe-haven event ( safe_haven = 1 ) if Bitcoin has a positive return while both Gold and the S&P 500 report negative returns. This framework captures the conditional migration to Bitcoin during potential stress periods in other asset classes. As shown in Table 1 above, less than one in seven trading days qualified under this classification, amounting to just 13.11%. This finding implies that safe-haven episodes are sporadic, which is consistent with the research of Bouri et al. ( 2017 ) and Corbet et al. ( 2020 ). Table 1 Distribution of Safe Haven vs Non-Safe Haven Days safe_haven Count % 0 (No) 1630 86.89 1 (Yes) 246 13.11 Table 2 presents examples of these episodes, particularly highlighting the timing from March to April 2020, when widespread panic due to COVID-19 appeared to induce significant market dislocations. Bitcoin’s divergence during these instances suggests a degree of decoupling from broader systemic selloffs. Table 2 Sample Days When Bitcoin acted as a Safe-Haven based on Divergence Logic Date Bitcoin_logret Gold_logret SP500_logret safe_haven 14-01-2020 0.068677 -0.001246 -0.001516 1 31-03-2020 0.002081 -0.031872 -0.016142 1 21-04-2020 0.003873 -0.004263 -0.031155 1 28-04-2020 0.003813 -0.003913 -0.005256 1 06-05-2020 0.032758 -0.011993 -0.007004 1 Note: Log returns are presented in decimal format. For example, 0.01 corresponds to a 1% daily return. To analyze the statistical behavior of divergence indicators, we present descriptive statistics on the clipped ratios of Bitcoin against Gold and the S&P 500 (Table 3 ). Both the btc_gold_ratio_clipped and the btc_sp500_ratio_clipped exhibit high kurtosis values (16.12 and 11.73, respectively), suggesting the presence of fat tails and significant divergence events. The negative skewness in both indicators indicates that upside divergence (i.e., positive divergence of Bitcoin under stress) is more pronounced than downside convergence. Table 3 Descriptive Statistics of Clipped Divergence Ratios between Bitcoin and Traditional Assets Variable Count Mean Std Min 25% 50% 75% Max Skewness Kurtosis btc_gold_ratio_clipped 1288 0.08 1.80 -10.0 -0.22 0.05 0.36 10.0 -0.25 16.12 btc_sp500_ratio_clipped 1288 0.03 2.14 -10.0 -0.14 0.11 0.48 10.0 -1.71 11.73 Table 4 analyzes the strength and nature of the relationship between divergence indicators and the safe_haven flag through Pearson and Spearman correlation coefficients. Although the correlations were weak (ranging from − 0.18 to -0.27), they showed consistent directional trends and were statistically significant. Notably, the Spearman values reinforce the idea of a nonlinear, threshold-dependent relationship between divergence and safe-haven classification. Table 4 Correlation of Divergence Indicators with Safe Haven Flag Divergence Indicator Pearson Correlation Spearman Correlation btc_gold_ratio_clipped -0.1837 -0.2766 btc_sp500_ratio_clipped -0.1858 -0.2742 Figure 1 presents a correlation heatmap of significant returns and macro variables. As anticipated, Bitcoin exhibits a weak correlation with both Gold and the S&P 500. Additionally, macro variables like CPI and FEDFUNDS reveal only minor correlations with Bitcoin, further supporting Kristoufek’s ( 2015 ) conclusions about Bitcoin’s detachment from traditional economic influences. Interestingly, the VIX exhibits a slight correlation with Bitcoin returns, suggesting that behavioral reactions to volatility may be a more significant factor in driving Bitcoin returns than changes in macroeconomic policy. These descriptive analytics support the paper’s modeling strategy: Bitcoin’s safe-haven characteristic is dependent, sporadic, and based on divergences; it is neither consistent nor can it be accounted for through standard or stable correlations with macroeconomic variables. Figure 2 illustrates the distribution of daily log returns for Bitcoin, Gold, and the S&P 500. The return distribution of Bitcoin is noticeably leptokurtic, featuring heavier tails, which highlights its high volatility and capacity for extreme fluctuations compared to traditional assets. This finding reinforces the view of Bitcoin as a high-risk investment, particularly given its tendency to experience sudden and abrupt price fluctuations. Figure 3 illustrates Bitcoin’s 30-day rolling volatility, emphasizing notable levels of persistent volatility clustering, particularly during times of macroeconomic shocks and broad intraday market declines. This reinforces the notion that Bitcoin’s volatility is a significant characteristic (e.g., btc_vol_30d ) in the predictive modeling framework, particularly given Bitcoin’s distinctive extreme volatility clustering style, as mentioned in Gkillas and Katsiampa ( 2018 ). Figure 4 illustrates the seasonal analysis of log returns for Bitcoin, Gold, and the S&P 500. In comparison, Bitcoin reveals no apparent seasonality or long-term trend; both Gold and the S&P 500 exhibit mild cyclicality. This supports Bitcoin’s unique nature and justifies the use of machine learning over traditional time series models. Figures 5 and 6 illustrate timelines that highlight the divergence in returns of Bitcoin compared to the S&P 500 and Gold, respectively. These figures suggest that Bitcoin can positively diverge from each market on its own, thereby supporting its potential as an asymmetric hedge in times of stress. Figure 7 merges both divergence patterns into a timeline, providing a visual depiction of the dual-dissociation logic applied to the safe-haven flag in this study. Additionally, it highlights distinct periods during which Bitcoin showed positive returns while both traditional assets declined, defining the safe-haven behavior that this study adopts. 4.1.2 Visual Divergence Diagnostics While the exploratory summaries provided valuable insights, further diagnostics were conducted to analyze the behavior of divergence metrics across safe-haven and non-haven dates. Figure 8 illustrates a distinct rightward shift in the distribution of Bitcoin-Gold divergence for safe-haven dates compared to non-haven dates. The density curve for safe-haven days reveals a longer and broader tail, suggesting that Bitcoin often outperforms Gold, especially during market turmoil, and with greater intensity. This reinforces the notion that diverging from traditional assets is a fundamental aspect of Bitcoin’s role as a safe-haven asset. Figure 9 illustrates the distribution of Bitcoin-S&P 500 divergence values across classifications of safe-haven and non-haven dates. During safe-haven dates, there is a noticeable shift towards higher divergence values, suggesting that Bitcoin often experiences a positive decoupling from equity markets in times of adversity. This trend reinforces Bitcoin’s potential as a conditional hedge against declines in equity markets. Figure 10 presents a density plot illustrating divergence, marked by vertical lines that indicate the mean divergence for each class. The data shows that observations of safe-haven exhibit a significantly higher mean divergence compared to non-haven days. This finding supports the notion that Bitcoin decouples more profoundly from the S&P 500 during periods when it is regarded as a safe haven. The distinction in central tendency adds statistical significance to our framework for classifying divergence. Figure 11 illustrates the distributions of the log return ratio of Bitcoin compared to the S&P 500, with a focus on its status as a safe haven. The safe-haven category exhibits a longer right tail and peaks further right than the non-haven category, indicating that Bitcoin tends to outperform equities when it serves as a safe haven. This asymmetric deviation from symmetry acknowledges the use of engineered ratio features for modeling purposes. The time-series plot in Fig. 12 displays the daily divergence values of Bitcoin from Gold and the S&P 500, with safe-haven events marked in red. There is a consistent correlation between safe-haven events and spikes in divergence values, which supports the temporal validity of the rule-based approach used in identifying safe-haven flags. This further reinforces the rationale for employing divergence logic to describe and model episodic safe-haven behavior in Bitcoin. 4.1.3 Macro-Condition Separation Diagnostics The assessment of CPI levels on both safe-haven and non-haven days revealed a significant overlap between the two categories, indicating that inflation is not the main factor influencing Bitcoin’s divergence behavior. This aligns with Kristoufek ( 2015 ), who noted Bitcoin’s separation from traditional inflation-related assets. As illustrated in Fig. 13 , we depict the distribution of VIX, which indicates equity market volatility. Safe-haven days typically showed markedly right-skewed distributions. While there was still significant overlap, the right skew suggests slightly heightened volatility conditions regarding Bitcoin as a safe haven, reinforcing the hypothesis that instances of safe-haven Bitcoin transactions are generally tied to increased uncertainty, as well as these clustered behaviors in digital assets (Gkillas & Katsiampa, 2018 ). Figure 14 shows the distribution of FEDFUNDS across the two classes. The nearly identical distributions suggest that interest rate policy has a minimal direct impact on safe-haven flag classification, further emphasizing what appears to be a nonlinear, event-driven, and largely independent safe-haven response to monetary policy levels. 4.2 Modeling Performance This study classifies Bitcoin’s role as a conditional safe haven by examining engineered divergence predictors, macroeconomic indicators, and market volatility signals. The dependent variable ( safe_haven ) is a binary response, defined through a rule-based label indicating instances when Bitcoin’s price rose while both Gold and the S&P 500 fell. We performed three classifications: Logistic regression, Random Forest, and XGBoost, to assess whether traditional linear classifiers, such as Logistic regression, can effectively capture the nonlinear divergence trajectories linked to safe-haven behavior, or if the predictive power of ensemble tree-based methods is superior. 4.2.1 Classifier Comparison Table 5 summarizes the model’s performance across five key metrics: accuracy, Recall, Precision, F1 Score, and Area Under the receiver operating characteristic curve (AUC). Among the three models, XGBoost initially excelled by effectively identifying rare safe-haven signals and achieving high recall and AUC scores, which led to its selection for further assessment of explainability. Table 5 Comparative Performance Summary of Logistic Regression, Random Forest, and XGBoost Model Accuracy Recall (Class 1) Precision (Class 1) F1 Score ROC AUC Logistic Regression 0.79 0.35 0.69 0.46 0.88 Random Forest 1 0.97 1 0.98 1 XGBoost 0.996 0.94 1 0.97 0.997 4.2.2 Confusion Matrix and ROC Curve To assess the classification performance, refer to the confusion matrix of the fitted XGBoost model in Table 6 . Among the 17 safe-haven instances in the testing set, 15 were accurately classified, and the model did not misclassify any additional instances as safe havens. Classification performance metrics are presented in Table 7 . Figure 15 illustrates the XGBoost model’s proficiency in detecting the minority class, as evidenced by an AUC of 0.997, indicating near-perfect performance. These assessments confirm that XGBoost maintains high sensitivity and overall predictive accuracy, even in the presence of class imbalance. Table 6 Confusion Matrix for XGBoost Predictions on the Test Set Predicted: Non-Haven (0) Predicted: Safe Haven (1) Actual: Non-Haven (0) 235 0 Actual: Safe Haven (1) 2 15 Table 7 Classification Report for XGBoost Predictions on the Test Set Class Precision Recall F1-Score Support Non-Haven (0) 0.99 1 1 235 Safe Haven (1) 1 0.88 0.94 17 Accuracy 0.99 252 Macro Average 1 0.94 0.97 252 Weighted Average 0.99 0.99 0.99 252 4.3 Explainability with SHAP We applied SHAP (SHapley Additive exPlanations) to the fitted XGBoost model to improve transparency and assess the role of each feature in determining the safe haven status of individual observations. SHAP calculates the marginal effect of every input feature for each prediction, providing both global importance rankings and local interpretability (Lundberg & Lee, 2017 ). This approach enhances transparency and aligns with contemporary definitions of explainable AI (XAI) by offering a data-driven rationale for the divergence-based features we developed earlier. Additionally, it supports fundamental XAI principles such as accountability and actionability (Doshi-Velez & Kim, 2017 ). Figure 16 showcases the global SHAP summary, highlighting that btc_sp500_ratio emerged as the most significant feature, followed by SP500_logret, Gold_logret , and btc_gold_ratio. This further suggests that Bitcoin’s performance during downturns is the main reason it is considered a safe-haven asset. Table 8 presents data on the top 10 features, ranked by their contribution as indicated by SHAP values. The SHAP beeswarm plot in Fig. 17 offers more profound insight into directional influence. Elevated btc_sp500_ratio values (the red dots to the right) consistently indicate positive SHAP values, enhancing the model’s likelihood of predicting a safe haven (flag = 1). Conversely, negative values from SP500_logret and Gold_logret (the blue dots on the left) drive predictions towards flag = 0, consistent with the initial rule-based divergence flag logic. This suggests that Bitcoin’s rise, occurring alongside declines in equity and Gold, is the key signal the model identifies as significant, as captured through both raw log returns and engineered ratios. Table 8 Top 10 Predictive Features Ranked by SHAP Importance Rank Feature Index Feature Mean(|SHAP|) 1 26 btc_sp500_ratio 2.77 2 5 SP500_logret 1.17 3 4 Gold_logret 1.10 4 25 btc_gold_ratio 1.04 5 9 btc_gold_divergence 0.86 6 27 btc_gold_ratio_clipped 0.64 7 10 btc_sp500_divergence 0.60 8 28 btc_sp500_ratio_clipped 0.19 9 23 btc_vs_gold_logret_ratio 0.18 10 24 btc_vs_sp500_logret_ratio 0.08 Each point indicates a single observation, where red denotes high feature values and blue indicates low values. Features such as btc_sp500_ratio and btc_gold_ratio enhance safe-haven classification, while decreases in SP500_logret and Gold_logret undermine it, thus supporting the divergence-based logic. Our results align with recent literature, providing initial evidence of nonlinear, episodic behavior in Bitcoin’s connection with traditional markets (Bouri et al., 2019 ; Yae & Tian, 2024 ). Bitcoin does not act as a stable, safe-haven asset with consistent hedging traits; instead, it functions as a conditional hedge that responds to relative return divergences rather than macroeconomic fundamentals, such as the volatility index (VIX) or monetary policy interest rates (FED FUNDS). 4.4 Comparative Modeling and Interpretation To assess the robustness and generalizability of the divergence-based safe-haven classification, we trained and evaluated three models: Logistic Regression, Random Forest, and XGBoost. All models were trained on the same balanced dataset and tested using stratified holdout and cross-validation methods. 4.4.1 Logistic Regression: Benchmark Interpretability Logistic regression served as the baseline model due to its interpretability and ease of use. The metrics show solid performance for class 0 (non-safe haven) with a precision of 0.99 and an accuracy of 0.88. For class 1 (safe-haven) detection, it achieved a precision of 0.35, a recall of 0.88, and an F1 score of 0.50. The ROC AUC score is robust at 0.95 (Table 9 ), while the mean section cross-validated AUC of 0.9516 ± 0.0069 across five folds suggests good generalization stability. Table 9 Comparative Classification Performance of Models Model Class Precision Recall F1-Score Support ROC AUC Logistic Regression 0 0.99 0.88 0.93 235 0.95 1 0.35 0.88 0.5 17 Macro Avg 0.67 0.88 0.72 252 Weighted Avg 0.9 0.88 0.89 252 Random Forest 0 0.99 1 1 235 1 1 1 0.88 0.94 17 Macro Avg 1 0.94 0.97 252 Weighted Avg 0.99 0.99 0.99 252 XGBoost (from earlier phase) - - - - - 0.97 (AP from PR curve) This shows that a linear model can still identify nonlinear divergence patterns when the features are well-engineered. However, the lower precision for class 1 suggests that logistic regression may over-predict the safe-haven condition in specific edge cases. 4.4.2 Random Forest: Nonlinear Ensemble Performance The Random Forest classifier greatly exceeded logistic regression, achieving perfect precision and recall scores (1.00) for class 1 and an overall test set accuracy of 0.99. Additionally, the ROC AUC score reflects a flawless classification boundary (1.00). These outcomes highlight the nonlinear and interaction-driven characteristics of safe-haven episodes, which tree-based ensembles can uniquely capture. 4.4.3 Model Comparison via Precision–Recall Curves To assess model performance under conditions of class imbalance, we generated Precision-Recall (PR) curves for all three models (Fig. 18 ). In summary, XGBoost achieved a commendable average precision (AP) of 0.97, while Random Forest excelled with an AP of 1.00, and Logistic Regression recorded an AP of 0.53. These findings further support the value of ensemble modeling in capturing high-risk divergence behavior and corroborate previous calls for tree-based modeling approaches for cryptocurrency volatility and hedging (Bouri et al., 2019 ; Abdalhammed et al., 2022 ; Šestanović & Kalinić Milićević, 2023 ). Additionally, Mallqui and Fernandes ( 2019 ) noted that Random Forests were valuable in modeling daily Bitcoin prices. 4.5 Robustness Checks and Prescriptive Stratifications 4.5.1 Cross-Validation Robustness To evaluate the model’s generalizability and prevent overfitting, we conducted a 5-fold cross-validation using the AUC metric on the Random Forest model. The results demonstrated exceptional consistency across the folds, with each fold yielding an AUC of 1.0 and a standard deviation of 0. The outcomes were uniform across all folds, suggesting that the model's structure and the dependent relationships among features should remain reliably accurate across different partitions of the dataset. This conclusion aligns with the prevalence of similar features across combinations in the SHAP analysis and is consistent with the validation results from the original dataset of the XGBoost model. 4.5.2 Prescriptive Stratification for Decision Support Transitioning from binary classification, the model’s probabilistic output has been segmented into three confidence areas (representing three actionable decisions probabilistically): High Certainty Safe-haven (P ≥ 0.8) Moderate Certainty (0.5 ≤ P < 0.8) Low Certainty / No Signal (P < 0.5) Based on these thresholds, the majority of predictions (237 out of 252) remained in the low-certainty zone, with 15 confidently marked as safe-haven cases. Figure 19 displays this classification, emphasizing the episodic and rare instances of Bitcoin’s safe-haven signals. This probability classification offers a more practical and understandable approach for portfolio managers; we not only deliver binary outputs but also convey a level of confidence in those results. 4.5.3 Threshold-Specific Precision–Recall Analysis The analysis of the model’s output focused on prescriptive performance by examining rates starting at the minimum threshold of 0.3 and evaluating higher thresholds up to 0.9. As shown in Table 10 , precision was flawless (1.00) across all thresholds, while recall improved with decreasing thresholds. Specifically, a threshold of 0.3 yielded the highest recall (0.94) and an F1 score, representing a balance between confidence and sensitivity, of 0.97. Therefore, these isolated results instill confidence in the model’s reliability in scenarios where failing to identify safe-haven signals incurs significantly higher costs than false alarms, as previously mentioned in crises (Kristoufek, 2015 ; Corbet et al., 2020 ). Table 10 Threshold-Specific Evaluation Metrics for Safe Haven Classification (Random Forest) Threshold TP FP TN FN Precision Recall F1 Score 0.9 14 0 235 3 1 0.82 0.9 0.8 15 0 235 2 1 0.88 0.94 0.7 15 0 235 2 1 0.88 0.94 0.6 15 0 235 2 1 0.88 0.94 0.5 15 0 235 2 1 0.88 0.94 0.4 15 0 235 2 1 0.88 0.94 0.3 16 0 235 1 1 0.94 0.97 5. Conclusion This study presents a divergence-based, explainable machine-learning framework for assessing Bitcoin’s function as a conditional safe-haven asset. By developing a rule-based classification flag that identifies instances when Bitcoin rises while both Gold and the S&P 500 decline, we provide a replicable and data-driven method for capturing flight-to-safety behavior during macro-financial stress. Empirical results reveal that XGBoost consistently surpasses both logistic regression and random forest in identifying these episodic safe haven occurrences. The implementation of SHAP (SHapley Additive exPlanations) enables the transparent interpretation of model predictions, highlighting that Bitcoin’s divergence from traditional asset returns is the primary factor influencing safe-haven behavior. These findings support the idea that Bitcoin’s hedge-like behavior is not constant but instead conditional and influenced by stress. In addition to accuracy, the integration of SHAP interpretability and probabilistic classification zones enhances the model’s prescriptive relevance. This facilitates practical application in institutional environments, especially for those pursuing regulatory-compliant AI models and decision-support systems to navigate financial uncertainty. Declarations Conflict of interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Declaration of generative AI and AI-assisted technologies in the writing process During the preparation of this work, the author used Grammarly and Litmaps to check the English grammar and logical framework and extesnive liteature review. After using this tool/service, the author reviewed and edited the content as needed and took full responsibility for the content of the publication. Ethics Declaration This study did not involve human participants, personal data, or confidential information. Therefore, ethical approval was not required. Funding This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors. Author Contribution M.B.R. conceptualized the research design, conducted the imputation benchmarking experiments, and performed the SHAP-based interpretability analysis. M.B.R. also wrote the main manuscript text, curated all figures and tables, and ensured methodological rigor through statistical testing. 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Identification of the optimal neural network architecture for prediction of Bitcoin return. Informatica, 36(1), 175–196. https://doi.org/10.15388/24-INFOR561 Shahzad, S. J. H., Bouri, E., Roubaud, D., Kristoufek, L., & Lucey, B. M. (2019). Is Bitcoin a better safe-haven investment than Gold and commodities? International Review of Financial Analysis, 63, 322–330. https://doi.org/10.1016/j.irfa.2019.01.002 Shaikh Sarfarazurrehman. (2024). AI/ML Case Study: Multi-Domain Asset Class Risk Prediction (Equities, Crypto, and Real-Estate) . Journal of Computational Analysis and Applications (JoCAAA), 33(05), 1746–1765. Retrieved from https://eudoxuspress.com/index.php/pub/article/view/2762 Shen, Z., Wan, Q., & Leatham, D. J. (2021). Bitcoin return volatility forecasting: A comparative study between GARCH and RNN. Journal of Risk and Financial Management, 14(7), 337. https://doi.org/10.3390/jrfm14070337 Todorovska, A., Peshov, H., Rusevski, I., Vodenska, I., Chitkushev, L. T., & Trajanov, D. 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Cite Share Download PDF Status: Published Journal Publication published 25 Oct, 2025 Read the published version in Quality & Quantity → Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6909016","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":484970259,"identity":"99d27327-51d1-4562-bb57-c7dda702c224","order_by":0,"name":"Manjunath B R","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA0klEQVRIiWNgGAWjYJACAwjBw8DwgRQtEiAtjDMSSLAJrIWZhxgtuu1nDxTz7rCrM2fgPfbZ9oeNPIPYGQO8WszO5CUY855JlrBs4EuenZOQZtggnYbfLrMDOQbGvG3MEgYHeIyZcxIOJzBIJx/Ar+X8G5CWeogWi4T/QC2JDfi13ADbchiihSHhABG23HhjYDi37bjkhsN8yYw9acmGbQT9cj7HzOBtWzW/wfHewww/bOzk+aVz8IcYELBBVDDDuITUg9Q+IELRKBgFo2AUjGQAANVcPMWH7me5AAAAAElFTkSuQmCC","orcid":"","institution":"Monterrey Institute of Technology and Higher Education","correspondingAuthor":true,"prefix":"","firstName":"Manjunath","middleName":"B","lastName":"R","suffix":""}],"badges":[],"createdAt":"2025-06-17 00:38:15","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6909016/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6909016/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11135-025-02424-z","type":"published","date":"2025-10-25T16:16:23+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":86762086,"identity":"2c954f7b-abc2-4e91-b01a-ccd39d1c20dc","added_by":"auto","created_at":"2025-07-15 10:30:28","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":79383,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eCorrelation Heatmap of Log Returns, Divergence Indicators, and Macroeconomic Variables\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image1.png","url":"https://assets-eu.researchsquare.com/files/rs-6909016/v1/b068edb1298f6d72b4646c75.png"},{"id":86762093,"identity":"630a68b2-12c1-4baf-98da-67d2df79428c","added_by":"auto","created_at":"2025-07-15 10:30:28","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":57581,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDistribution of Daily Log Returns for Bitcoin, Gold, and S\u0026amp;P 500\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image2.png","url":"https://assets-eu.researchsquare.com/files/rs-6909016/v1/0306a10b5a8c7b07a8dbd37c.png"},{"id":86763868,"identity":"7d875e31-47ba-4757-b939-6e10c1404907","added_by":"auto","created_at":"2025-07-15 10:46:28","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":62516,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eBitcoin 30-Day Rolling Volatility (Volatility Persistence Feature)\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image3.png","url":"https://assets-eu.researchsquare.com/files/rs-6909016/v1/0fe59a4e7a9ab587b6d75cb6.png"},{"id":86762962,"identity":"2333d9ac-5683-46f9-8e32-0c9124d20bf4","added_by":"auto","created_at":"2025-07-15 10:38:28","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":280441,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSeasonal Decomposition of Log Returns for Bitcoin, Gold, and S\u0026amp;P 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Return Divergence\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image6.png","url":"https://assets-eu.researchsquare.com/files/rs-6909016/v1/db26df41d36926f517c384b0.png"},{"id":86762960,"identity":"ca277885-0f35-45e6-ac90-b14d786fa9e7","added_by":"auto","created_at":"2025-07-15 10:38:28","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":115857,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eCombined Divergence of Bitcoin Against Gold and S\u0026amp;P 500\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image7.png","url":"https://assets-eu.researchsquare.com/files/rs-6909016/v1/19084c5545b262d8694b6358.png"},{"id":86762095,"identity":"a2a75771-52d1-46fd-8997-6dba0ec276f7","added_by":"auto","created_at":"2025-07-15 10:30:28","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":50953,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDistribution of Bitcoin-Gold Divergence Across Safe Haven and Non-Haven Days\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image8.png","url":"https://assets-eu.researchsquare.com/files/rs-6909016/v1/92ca5905f84d13d6cc21f6b8.png"},{"id":86762965,"identity":"5c5b0747-3ae4-4ee0-92e4-8d440c69edf1","added_by":"auto","created_at":"2025-07-15 10:38:28","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":49552,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDistribution of Bitcoin–S\u0026amp;P 500 Divergence Across Safe Haven and Non-Haven 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11","display":"","copyAsset":false,"role":"figure","size":43454,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDistribution of Bitcoin–S\u0026amp;P 500 Log Return Ratio by Safe Haven Classification\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image11.png","url":"https://assets-eu.researchsquare.com/files/rs-6909016/v1/843d37835cad61f8fb153790.png"},{"id":86762108,"identity":"522f16ff-a707-429f-bb6d-00e6c307c9cc","added_by":"auto","created_at":"2025-07-15 10:30:28","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":146933,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eTime Series of Bitcoin Divergence from Gold and S\u0026amp;P 500 with Safe Haven Event 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14","display":"","copyAsset":false,"role":"figure","size":50621,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDistribution of Federal Funds Rate Across Safe Haven and Non-Haven Days\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image14.png","url":"https://assets-eu.researchsquare.com/files/rs-6909016/v1/38e3f3ebbd0b90155ea67de1.png"},{"id":86763874,"identity":"7e5d66d4-d563-45b8-b72c-e72b1a121952","added_by":"auto","created_at":"2025-07-15 10:46:29","extension":"png","order_by":15,"title":"Figure 15","display":"","copyAsset":false,"role":"figure","size":25982,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eROC Curve for XGBoost Classifier\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image15.png","url":"https://assets-eu.researchsquare.com/files/rs-6909016/v1/325037bc9becb3d33b81f9b8.png"},{"id":86762112,"identity":"523a2e6f-82f0-4e7d-a036-b178739d1baa","added_by":"auto","created_at":"2025-07-15 10:30:29","extension":"png","order_by":16,"title":"Figure 16","display":"","copyAsset":false,"role":"figure","size":52773,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eGlobal SHAP Feature Importance for Safe Haven Prediction Using XGBoost\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image16.png","url":"https://assets-eu.researchsquare.com/files/rs-6909016/v1/fa8ad1fbf4712937980e54f6.png"},{"id":86762116,"identity":"521639b9-15f9-4ba3-b6db-4ec6bfc3acb7","added_by":"auto","created_at":"2025-07-15 10:30:29","extension":"png","order_by":17,"title":"Figure 17","display":"","copyAsset":false,"role":"figure","size":84242,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSHAP Beeswarm Plot for Directional Feature Impact on Safe Haven Prediction\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image17.png","url":"https://assets-eu.researchsquare.com/files/rs-6909016/v1/bd223feee5489ea7db92c23a.png"},{"id":86764631,"identity":"6d6e9314-e574-41fb-9a01-d2af48520a3f","added_by":"auto","created_at":"2025-07-15 10:54:29","extension":"png","order_by":18,"title":"Figure 18","display":"","copyAsset":false,"role":"figure","size":38128,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eComparison of Logistic, RF, and XGBoost models highlighting Random Forest and XGBoost's superior performance on minority class detection.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image18.png","url":"https://assets-eu.researchsquare.com/files/rs-6909016/v1/f6a7cb01f27deb5ec3a82143.png"},{"id":86762109,"identity":"8c8de50c-11d8-4bcb-b06b-1add3a83b9ab","added_by":"auto","created_at":"2025-07-15 10:30:28","extension":"png","order_by":19,"title":"Figure 19","display":"","copyAsset":false,"role":"figure","size":31039,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDistribution of Predicted Probabilities from Random Forest Model with Prescriptive Thresholds\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image19.png","url":"https://assets-eu.researchsquare.com/files/rs-6909016/v1/8dbc4655363f1dcacf8bd7b6.png"},{"id":94490045,"identity":"af692fa5-fbc3-473d-af87-b88a0340c621","added_by":"auto","created_at":"2025-10-27 17:07:12","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4031104,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6909016/v1/5411e45f-6ac8-489c-ae77-2acdc30c18b3.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Classifying Bitcoin’s Safe Haven Role Using Explainable AI: Evidence from US Macroeconomic Stress Episodes","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eIn the face of increasing macroeconomic uncertainty, characterized by inflationary shocks, aggressive monetary tightening, and global crises such as the COVID-19 pandemic, investors are turning to resilient assets that protect their capital during downturns in traditional markets. Traditionally, safe-haven assets such as Gold and sovereign bonds have provided this downside protection.\u003c/p\u003e\u003cp\u003eA safe haven, as described by Baur and Lucey (\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2010\u003c/span\u003e), refers to an asset that is either uncorrelated or negatively correlated with a risk asset during periods of severe market stress. While the traditional understanding of safe haven behavior relies on these uncorrelated or negatively correlated responses in times of systemic stress, we adopt a divergence-based labeling approach, designating Bitcoin as a conditional safe haven exclusively when its value appreciates. At the same time, both Gold and the S\u0026amp;P 500 fall, as this shows a clear and observable trend in investor behavior, with funds shifting away from traditional hedges and high-risk options. The potential for Bitcoin to act as a conditional safe haven, particularly during periods of US economic and policy-driven turmoil, has garnered attention due to its decentralized nature, limited supply, and algorithmic creation (Shahzad et al., \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Umar et al., \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eThis study focuses on the timeframe from January 2020 to March 2025, a period characterized by significant changes in US policy. These changes include the COVID-19 market crash, post-pandemic inflation, and the Federal Reserve\u0026rsquo;s stringent interest rate hikes. Importantly, our analysis encompasses not only financial crashes but also recurrent instances of macroeconomic volatility driven by policy, such as unexpected inflation, interest rate fluctuations, and tapering announcements, as observed by Choi et al. (\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). These factors have been recognized as critical sources of stress in today\u0026rsquo;s financial markets.\u003c/p\u003e\u003cp\u003eBitcoin\u0026rsquo;s appeal theoretically lies in its resistance to inflation and decentralization; however, the evidence remains ambiguous. Early studies (Dyhrberg, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2016a\u003c/span\u003e) identified hedging traits similar to those found in Gold and traditional currencies. However, subsequent research has shown that Bitcoin exhibits pronounced volatility, susceptibility to contagion, and a positive correlation with stocks during market crises (Griffin \u0026amp; Shams, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). These fluctuations suggest that Bitcoin\u0026rsquo;s status as a safe haven is neither stable nor reliable; it tends to emerge only under specific macro-financial conditions influenced by liquidity shocks, policy uncertainties, and investor sentiment (Yae \u0026amp; Tian, \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Cheng \u0026amp; Yen, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Moreover, Bitcoin\u0026rsquo;s high volatility challenges its image as a typical safe haven, especially when compared to stable government bonds or traditional currencies. However, its relevance is still possible in certain divergence instances.\u003c/p\u003e\u003cp\u003eNumerous advanced econometric models, including wavelet decompositions, quantile regressions, and co-explosivity models (Bouri et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2019\u003c/span\u003e), have explored these interaction effects. However, they often struggle to effectively model the nonlinear and adaptive relationships that are present in volatile assets, such as cryptocurrencies. Consequently, more studies are turning to deep learning and AI methods, as these approaches are better equipped to handle chaotic financial time series (Fawaz et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Lahmiri \u0026amp; Bekiros, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2019\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eArchitectures such as Long Short-Term Memory (LSTM) and Convolutional Neural Network (CNN) have significantly improved Bitcoin price forecasting (Li \u0026amp; Dai, \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Livieris et al., \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Ji et al., \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Nonetheless, there is limited research on these technologies within macro-integrated classification systems that aim to evaluate Bitcoin as a safe-haven asset. The integration of macroeconomic indicators, such as the Consumer Price Index (CPI) and the Fed Funds Rate, along with sentiment measures like the Volatility Index (VIX), into AI models to analyze behavioral responses to U.S. policy shocks has been rarely examined (Shen et al., \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Paule-Vianez et al., \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Recent improvements in this field (Bianchi et al., 2021; Lee, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) have enhanced forecasting precision by utilizing attention-based additive methods and hybrid deep learning frameworks, thereby providing more accurate explanations for volatility in predictive trading models. These advancements indicate a transition from simple machine learning to more interpretable and reliable decision-making models.\u003c/p\u003e\u003cp\u003eMany recent studies prioritize correlation metrics while overlooking the advantages of explainable machine learning classifiers. These classifiers can leverage probabilistic divergence behavior instead of merely tracking coincident movements (Šestanović \u0026amp; Kalinić Milićević, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Kim et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). A divergence-style framework, such as when Bitcoin rises while Gold and stocks decline, illustrates shifts in investor preferences away from traditional stores of value, including assets perceived as safe havens against extreme risks, like equity and commodities. This viewpoint facilitates a deeper understanding of genuine capital substitution and enables a systematic classification that exceeds simple correlation. The lack of interpretability significantly hampers its applicability in policy-making and institutional risk management. SHapley Additive exPlanations (SHAP) is increasingly recognized as the key standard for interpretability, enabling regulatory bodies to monitor models that influence decision-making across all areas of financial services (Kumar \u0026amp; Mittal, 2022; Zhang \u0026amp; Li, 2023). Recent applications have demonstrated the effectiveness of SHAP in uncovering and quantifying nonlinear relationships among asset returns, volatility, and policy shifts, thereby enhancing the necessary transparency for robust decision-making in critical financial sectors (Lundberg \u0026amp; Lee, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). Its expanding use is forging a connection for AI predictions, where economic principles still hold, and investor behavior can be clarified during times of uncertainty.\u003c/p\u003e\u003cp\u003eTo empirically validate this divergence theory, we are establishing a supervised learning classification framework that utilizes macro-sensitive features and interpretable AI to identify safe haven episodes and their key drivers.\u003c/p\u003e\u003cp\u003e\u003cb\u003eThis paper makes five key contributions\u003c/b\u003e:\u003c/p\u003e\u003cp\u003e\u003col\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eIt proposes a framework for divergence-based labeling that recognizes Bitcoin as a conditional safe haven when it rises, while both Gold and the S\u0026amp;P 500 decline, signaling capital flight from conventional markets.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eIt creates macro-informed features that utilize rolling volatility, lagged macroeconomic signals, and return divergence ratios to reflect market stress and changes in behavior across different policy regimes.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eIt implements and benchmarks XGBoost, a robust ensemble model, against random forest and logistic regression classifiers.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eIt employs SHAP to rank and elucidate the factors influencing safe haven predictions, underscoring the importance of explainability in economic and policy contexts.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eIt introduces a prescriptive probability banding system that allows risk managers to interpret model outputs (e.g., high-certainty versus low-certainty safe haven events) for real-time asset allocation.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003c/ol\u003e\u003c/p\u003e\u003cp\u003eTogether, these contributions form a new, transparent, and actionable framework that links financial theory, interpretable AI, and macroeconomic factors, emphasizing Bitcoin\u0026rsquo;s potential status in portfolios during periods of crisis amid policy uncertainty. While we focus on the Gold as a traditional benchmark, it is essential to note that US Treasuries are often regarded as the quintessential safe-haven asset, especially during times of systemic crises and policy shocks (Baur \u0026amp; Lucey, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Baur \u0026amp; McDermott, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). Due to variations in liquidity profiles, yield dynamics, and market behavior, US Treasuries were excluded from our divergence-based operational framework. However, we recognize this as a significant limitation and suggest its incorporation as a beneficial extension for future research.\u003c/p\u003e"},{"header":"2. Literature Review","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003e2.1 Bitcoin as a Safe Haven: A Mixed Narrative\u003c/h2\u003e\u003cp\u003eBaur and Lucey (\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2010\u003c/span\u003e) define a safe haven as an asset that maintains or appreciates during severe market stress. This differs from a hedge, which is effective in normal market conditions, and a diversifier, which only slightly mitigates risk. Understanding this distinction is crucial, as many studies mix these terms, resulting in unclear interpretations of Bitcoin\u0026rsquo;s function.\u003c/p\u003e\u003cp\u003eRecent research has explored Bitcoin\u0026rsquo;s role as a safe-haven asset, producing mixed results. For instance, Liu \u0026amp; Yuan (\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) reassessed the crypto safe-haven hypothesis by analyzing Bitcoin against both fiat currencies and Treasuries during periods of monetary tightening, uncovering behaviors influenced by volatility clustering and investor flows. Bouri et al. (\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) and Dyhrberg (\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2016b\u003c/span\u003e) were early proponents of the idea that Bitcoin exhibits partial hedging behavior; however, this behavior is affected by structural breaks and volatility clustering. In a similar vein, Shahzad et al. (\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) employed dynamic copula and Markov-switching techniques to uncover regime-specific dependence structures between Bitcoin and traditional safe-haven assets. However, much of the existing safe haven literature focuses on US government bonds, mainly Treasuries, as the standard asset during episodes of global financial stress. Baur and McDermott (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2010\u003c/span\u003e), among others, note that Treasuries exhibit a steady inverse correlation with equities and high liquidity in crises. Our decision to exclude US Treasuries from our modeling approach results from our emphasis on high-frequency divergence signals involving crypto and commodity assets, and we recognize this as a structural limitation of our analytical reach.\u003c/p\u003e\u003cp\u003eUmar et al. (\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) investigated Bitcoin\u0026rsquo;s hedge functionality using wavelet quantile-on-quantile analysis, incorporating the US Partisan Conflict Index (PCI) and Economic Policy Uncertainty (EPU). Their findings indicate that Bitcoin\u0026rsquo;s safe-haven characteristics were quantile-specific, asymmetric, and varied over time, with evidence of bidirectional feedback during economic stress events, such as elections and the COVID-19 pandemic. Yae and Tian (\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) introduced a novel method for analyzing upward price momentum in Bitcoin. They observed a decoupling of equities, which they linked to passive institutional rebalancing. The authors discovered that a 0.1 drop in the correlation between Bitcoin and the S\u0026amp;P 500 forecasted a 1.5% chance of a positive return the following day. They emphasized that this trend did not hold for Gold or treasuries.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\u003ch2\u003e2.2 Machine Learning and Deep Learning in Crypto Forecasting\u003c/h2\u003e\u003cp\u003eMost conventional econometric methods (such as GARCH and VAR) struggle to fully capture Bitcoin\u0026rsquo;s distinct nonlinearities, long memory, and structural breaks. This limitation creates opportunities for advanced learning models to develop. Li and Dai (\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) proposed a hybrid model that merges convolutional neural networks with long short-term memory (CNN-LSTM) and incorporates macro-financial and sentiment indicators like the S\u0026amp;P 500, oil prices, Baidu Index, and Fed Funds Rate. The CNN-LSTM hybrid model outperformed standalone CNN, LSTM, and ANN methods, as well as those focused solely on short-term predictions. These findings demonstrate that the combination of convolutional pattern recognition and LSTM enhances the analysis of temporal sequences.\u003c/p\u003e\u003cp\u003eŠestanović and Kalinić Milićević (\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2025\u003c/span\u003e) performed a regime-aware analysis utilizing the Bai\u0026ndash;Perron methodology to categorize markets into bullish, bearish, and volatility regimes. Their integrated feature framework, comprising tweets, VIX, S\u0026amp;P 500, and Google Trends, reveals that CNNs are most effective during downturns, LSTMs thrive in uptrends, and FFNNs excel in volatile conditions.\u003c/p\u003e\u003cp\u003eJang and Lee (\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) introduced a Bayesian Neural Network (BNN) method to forecast Bitcoin prices. This technique integrates blockchain metrics, such as hash rate and transaction volumes, with macroeconomic indicators. They evaluated this methodology in real time, utilizing walk-forward validation, which steadily advances over time to yield precise predictions. Their approach surpassed both SVR and linear models. While its primary focus is price forecasting, it also provides a solid framework for safe-haven classification.\u003c/p\u003e\u003cp\u003eAbdalhammed et al. (\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) analyzed the Vanilla LSTM model in an uncertain environment that restricted the use of historical data, confirming the model\u0026rsquo;s robustness when dealing with limited datasets. They also incorporated GARCH solutions, connecting their model\u0026rsquo;s application to market efficiency. In a similar vein, Atsalakis et al. (\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) utilized PATSOS, a closed-loop neuro-fuzzy system that combines an adaptive neuro-fuzzy inference system (ANFIS) with an artificial neural network, achieving a hit rate of 63.22% and delivering returns 71% above the buy-and-hold strategy. This accomplishment represents a significant advancement, showcasing clarity and factuality about its comprehensiveness while exploring new methods for effectively integrating measures and data in response to news events.s\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\u003ch2\u003e2.3 Divergence Logic and Risk Prediction\u003c/h2\u003e\u003cp\u003eThe literature frequently discusses inter-asset divergence, which refers to the phenomenon where asset classes move in opposite directions, to help understand capital reallocation across different markets. Bouri et al. (\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2020a\u003c/span\u003e) and Guesmi et al. (\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) noted that such a divergence pattern indicates a risk-off market. The model proposed in this research supports the notion of Bitcoin as a safe haven, with rising Bitcoin prices accompanied by falling Gold and S\u0026amp;P 500 values, which strengthens this assertion. Additionally, Li and Dai (\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) demonstrated that external macroeconomic factors, such as the Fed Funds rate, oil prices, and equity returns, play a significant role in enhancing the accuracy of forecasting the dependent variable. By incorporating volatility indicators from the derived values (such as rolling standard deviations) and ratios of divergences, we can create a more detailed and conditional feature set for analysis.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\u003ch2\u003e2.4 Explainable AI and SHAP: Enhancing Financial Model Transparency\u003c/h2\u003e\u003cp\u003eAs neural networks evolve, the issue of transparency becomes increasingly crucial. Recently, SHAP (Lundberg \u0026amp; Lee, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) has emerged as the foremost technique for interpreting AI models in the finance industry. In their empirical study, Šestanović and Kalinić Milićević (\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) demonstrated how SHAP can inform the development of price predictions and highlighted the significant impact of sentiment and non-economic volatility on forecasts derived from neural networks. Nevertheless, SHAP remains underutilized in classification models for crypto risk modeling, such as divergence-based safe-haven forecasting. Additionally, SHAP guarantees variation in feature attribution, along with local consistency and local accuracy (Lundberg \u0026amp; Lee, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2017\u003c/span\u003e), setting it apart from competing feature attribution methods. This includes documenting the importance of features like the VIX, divergence, and lagged volatility through SHAP classification. This methodological framework helps to address the existing gap by improving transparency in crypto finance while meeting regulatory disclosure obligations.\u003c/p\u003e\u003cp\u003eRecent studies, such as those by Baklanova et al. (\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), Shaikh (2024), and Todorovska et al. (\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), employ SHAP to identify factors influencing the cryptocurrency market. These researchers explain their models through weights associated with economic events, including liquidity constraints, news sentiment, and macro spillovers. The factors highlighted in these studies are expected to further the application of SHAP in asset classification and influence investors\u0026rsquo; risk perceptions.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\u003ch2\u003e2.5 Gaps and Our Contribution:\u003c/h2\u003e\u003cp\u003eDespite notable progress in cryptocurrency research, four main gaps remain in understanding Bitcoin\u0026rsquo;s role as a conditional safe haven:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eInadequate classification frameworks relying on macro indicators\u003c/b\u003e: Numerous earlier studies (Bouri et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Shahzad et al., \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) focus on correlation, tail dependence, or wavelet decompositions; however, they largely overlook rule-based, ex-ante frameworks that integrate macroeconomic indicators (CPI, Fed Funds Rate) and market sentiment (VIX).\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eEmphasize price predictions over risk-role classifications\u003c/b\u003e: Numerous earlier studies, such as those by Ji et al. (\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) and Livieris et al. (\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2021\u003c/span\u003e), have focused on forecasting Bitcoin prices but have neglected its role as a conditional hedge during periods of systemic macro-financial stress.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eEmphasizing price prediction over risk-role classification\u003c/b\u003e: Earlier studies have focused on forecasting Bitcoin prices (e.g., Ji et al., \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Livieris et al., \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) without categorizing its behavior as a conditional hedge during periods of systemic macro-financial stress.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eLack of divergence-driven safe haven reasoning\u003c/b\u003e: Limited research investigates Bitcoin\u0026rsquo;s ascent while Gold and equities decline, overlooking capital flight trends observed in times of crisis.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eInsufficient integration of explainable AI (XAI)\u003c/b\u003e: Although ML models are utilized in crypto forecasting (e.g., Li \u0026amp; Dai, \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2020\u003c/span\u003e), few studies implement SHAP or similar XAI methods to clarify the factors influencing predictions, which compromises transparency for institutional adoption.\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003eThis study makes five significant contributions to the literature:\u003c/p\u003e\u003cp\u003e\u003col\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eMacro-Informed Divergence Logic\u003c/b\u003e: We propose a rule-based framework that is sensitive to macroeconomic conditions, classifying Bitcoin as a conditional safe haven when its value increases, while Gold and the S\u0026amp;P 500 experience concurrent drawdowns.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eComprehensive Feature Engineering\u003c/b\u003e: Our dataset encompasses divergence metrics, macroeconomic indicators (such as the CPI and Fed Funds), and market sentiment (as measured by the VIX), reflecting economic stress and investor uncertainty in response to US policy shocks.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eEffective Supervised Learning Models\u003c/b\u003e: We evaluate and compare XGBoost with Random Forest and Logistic Regression to identify safe-haven events, showing better results in both recall and AUC.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eSHAP-based Interpretability\u003c/b\u003e: We utilize SHAP to reveal both global and local feature contributions, thereby enhancing model transparency and facilitating a connection between predictions and economic behavior.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003ePrescriptive Confidence Stratification\u003c/b\u003e: We present a probabilistic decision support system that organizes predictions into actionable levels of safe-haven confidence, providing practical utility for institutional investors.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003c/ol\u003e\u003c/p\u003e\u003cp\u003eAlthough the study examines divergence from the Gold and S\u0026amp;P 500 indices, it does not account for US Treasuries, which are commonly viewed as benchmark safe-haven assets. This omission is acknowledged as a limitation and presents a valuable opportunity for future research to extend the divergence-based classification to fixed-income instruments.\u003c/p\u003e\u003cp\u003eTogether, these insights connect theory, machine learning, and explainable AI to present a new, transparent method for understanding Bitcoin\u0026rsquo;s fluctuating characteristics as a safe haven. The logic of divergence is based on the capital substitution theory. As conventional assets decline and Bitcoin rises, it suggests a potential shift towards digital alternatives during times of systemic turmoil.\u003c/p\u003e\u003c/div\u003e"},{"header":"3. Research Methodology","content":"\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\u003ch2\u003e3.1 Data Acquisition and Preprocessing\u003c/h2\u003e\u003cp\u003eThis research utilizes daily financial and macroeconomic data spanning from January 1, 2020, to March 31, 2025. This timeframe encompasses various global shocks, such as the COVID-19 pandemic, spikes in inflation, and shifts in policy rates. The daily frequency was chosen to capture the more nuanced divergence dynamics of Bitcoin compared to traditional safe-haven assets during periods of heightened turmoil.\u003c/p\u003e\u003cp\u003eThe selected sample period incorporates several systemic macro-financial shocks that influenced investor behavior, market volatility, and asset allocation. These shocks consist of:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eThe onset of the COVID-19 crisis and the swift global fiscal and monetary measures taken in early 2020 (Bouri et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2020b\u003c/span\u003e).\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eThe ongoing rise in inflation and disruptions in supply chains throughout 2021 and 2022 (Cleveland Federal Reserve Bank, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eThe Federal Reserve\u0026rsquo;s steep interest rate increases and quantitative tightening policies started in March 2022 (Board of Governors of the Federal Reserve System, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2022a\u003c/span\u003e, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2022b\u003c/span\u003e).\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eContinual geopolitical and policy uncertainties, which encompass stagflation risks and fluctuations in the US debt ceiling during 2024\u0026ndash;2025 (Congressional Research Service, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003eThese events led to repeated macro-policy stress regimes, making this timeframe an ideal time to analyze Bitcoin\u0026rsquo;s conditional safe-haven behavior during US policy-induced shocks.\u003c/p\u003e\u003cp\u003eThe variables and sources utilized are as follows:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eData for mid-market Bitcoin prices (BTC/USD), daily closing gold prices (XAU/USD), and the S\u0026amp;P 500 Index (SPX) is sourced from the Refinitiv Datastream platform, known for offering high-quality financial data series.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eThe CBOE Volatility Index (VIX) was obtained from Refinitiv to assess daily investor sentiment and systemic risk.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eIn this context, macroeconomic indicators include the Consumer Price Index (CPI) (CPIAUCSL) and the Federal Funds Effective Rate (FedFunds), both derived from Federal Reserve Economic Data (FRED).\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003eAs CPI and FedFunds are available monthly, both metrics were forward-filled to align with the daily granularity of the market data. This adhered to the established guidelines for mixed-frequency data (Aljinović et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). This method preserves the temporal integrity of the modeling process and avoids potential leakage that could result in misleading correlations.\u003c/p\u003e\u003cp\u003eTo ensure variance stability and enhance comparability among asset classes, all raw price series were converted into logarithmic returns through the following transformation (using Eq.\u0026nbsp;1):\u003c/p\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{r}_{t}=\\text{ln}\\left(\\frac{{P}_{t}}{{P}_{t-1}}\\right)\\)\u003c/span\u003e\u003c/span\u003e -------(1)\u003c/p\u003e\u003cp\u003eWhere \u003cem\u003er\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e is the log return of the asset on day \u003cem\u003et\u003c/em\u003e, \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e represents the closing price of the asset at times \u003cem\u003et\u003c/em\u003e and \u003cem\u003et-1\u003c/em\u003e. This adjustment stabilizes variance and makes returns approximately stationary. This method stabilizes variance and offers insights into percentage changes (Gandal et al., \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). To test for stationarity in the transformed series, the Augmented Dickey-Fuller (ADF) test was conducted, confirming the suitability of using return-based features for time series classification (Šestanović \u0026amp; Kalinić Milićević, \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). There were no missing or incomplete values to impute from this dataset.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\u003ch2\u003e3.2 Binary Target Construction: Safe Haven Flag\u003c/h2\u003e\u003cp\u003eA novel binary classification target Y\u003csub\u003et\u003c/sub\u003e \u0026isin;{0,1} was engineered to reflect the safe haven behavior of Bitcoin (using Eq.\u0026nbsp;2)as follows:\u003c/p\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Y}_{t}\\:=\\:\\left\\{\\begin{array}{c}1\\\\\\:0\\end{array}\\right.\\:\\begin{array}{c}if\\:{r}_{t}^{BTC}\\:\u0026gt;\\:0\\:\\wedge\\:\\:{r}_{t}^{Gold\\:}\\:\u0026lt;\\:0\\:\\wedge\\:\\:{r}_{t}^{SPX}\\:\u0026lt;\\:0\\\\\\:Otherwise\\end{array}\\)\u003c/span\u003e\u003c/span\u003e ------- (2)\u003c/p\u003e\u003cp\u003eThis illustrates instances where Bitcoin\u0026rsquo;s returns rise, even as those of Gold and the S\u0026amp;P 500 decline or exhibit positive returns. This finding is consistent with the safe haven definitions based on divergence, as discussed in the literature (Paule-Vianez et al., \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Shahzad et al., \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2019\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eThe flag relies exclusively on daily-return data at time \u003cem\u003et\u003c/em\u003e, incorporating the asset prices at \u003cem\u003et\u003c/em\u003e and \u003cem\u003et-1\u003c/em\u003e. This approach ensures that the target label can be observed beforehand, independent of subsequent information, thus facilitating the acceptance of causal relationships within real-time classification systems. In this context, while we adopt a risk-off posture, it should not be considered \"hedging\" in the correlation sense (Baur \u0026amp; Lucey, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2010\u003c/span\u003e); instead, it frames our conditional flight-to-safety behavior within a rule-based structure. Although this divergence flag may indicate some short-term hedging activity, it ultimately hinges on the set threshold limit for the flag. A threshold-based flag provides a clear, reproducible, and easily interpretable signal in real time, reinforcing the idea that expectations represent the most effective way to showcase Bitcoin\u0026rsquo;s substitutive role during a downturn in an asset class.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\u003ch2\u003e3.3 Feature Engineering\u003c/h2\u003e\u003cp\u003eWe developed a formal list of characteristics, including inter-asset return differentials and macroeconomic indicators, to accurately model Bitcoin\u0026rsquo;s behavior as a potential safe haven during periods of divergence.\u003c/p\u003e\u003cdiv id=\"Sec12\" class=\"Section3\"\u003e\u003ch2\u003e3.3.1 Divergence Indicators:\u003c/h2\u003e\u003cp\u003eThe key defining variables are formulated as pair-wise return differentials between Bitcoin and traditional assets (using Eq.\u0026nbsp;3):\u003c/p\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:{Div}_{BTC\\:\\:-\\:Gold,t\\:}=\\:{r}_{t}^{BTC}\\:-\\:{r}_{t}^{Gold},\\:\\:\\:\\:\\:\\:{Div}_{BTC\\:-\\:SPX,t\\:}=\\:{r}_{t}^{BTC}\\:-\\:{r}_{t}^{SPX}\\)\u003c/span\u003e\u003c/span\u003e-------(3)\u003c/p\u003e\u003cp\u003eThese divergence measures consider directional discrepancies in asset returns and employ substitution theory within capital portfolios. Investors allocate funds across assets with varying risk profiles, utilizing substitution theory especially during volatile times. Additionally, previous studies indicate that hedging strategies and transitions to safer assets tend to happen when gold and equities face negative returns at the same time, serving as \"traditional hedge\" assets (Shahzad et al., \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Paule-Vianez et al., \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec13\" class=\"Section3\"\u003e\u003ch2\u003e\u003cb\u003e3.3.2 Lagged Macro Signals\u003c/b\u003e:\u003c/h2\u003e\u003cp\u003eTo include pertinent macro-financial context, the following lagged indicators were added (using Eq.\u0026nbsp;4):\u003c/p\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{CPI}_{t-1},\\:{VIX}_{t-1},\\:{FedFunds}_{t-1}\\)\u003c/span\u003e\u003c/span\u003e -------(4)\u003c/p\u003e\u003cp\u003eLagging offers models certainty that they rely exclusively on information available at decision time \u003cem\u003et\u003c/em\u003e, eliminating forward-looking bias. These elements are linked to inflationary pressures, market volatility, and the position of monetary policy, affecting asset substitution and the appeal of safe havens.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec14\" class=\"Section3\"\u003e\u003ch2\u003e3.3.3 Data Transformation and Normalization\u003c/h2\u003e\u003cp\u003eTo mitigate the impact of extreme return values, the features were winsorized according to the 95th percentile rule (Fawaz et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). This approach improved the original feature structure while simultaneously minimizing potential outliers and extreme returns. Subsequently, all relevant features were MinMax normalized (Li \u0026amp; Dai, \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2020\u003c/span\u003e), a crucial step for dimensionality reduction and ensuring compatibility with models that rely on gradient descent algorithms, such as XGBoost. These engineered features serve as a solid and economically interpretable basis for classifying safe haven behavior.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec15\" class=\"Section3\"\u003e\u003ch2\u003e3.3.4 Why Machine Learning Models?\u003c/h2\u003e\u003cp\u003eMost studies on safe haven assets mainly employed econometric models, including GARCH family models, Markov-switching models, quantile regressions, and threshold regressions (Bouri et al, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Shahzad et al, \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Although these econometric models provide valuable insights, they frequently encounter limitations arising from assumptions about stationarity, linearity, and their limited features.\u003c/p\u003e\u003cp\u003eIn contrast, machine learning algorithms such as XGBoost and Random Forest:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eIdentify nonlinear connections and interactions among engineered features, including divergence ratios, rolling volatilities, and macro lags.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eManage imbalanced datasets more efficiently.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eFacilitate real-time classification with scalability.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eMost importantly, it provides explainability through SHAP, offering actionable insights for financial decision-making.\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003eTherefore, ML provides predictive capabilities and transparency, addressing the shortcomings of conventional methods.\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Sec16\" class=\"Section2\"\u003e\u003ch2\u003e3.4 Modeling Approaches\u003c/h2\u003e\u003cp\u003eWe analyzed Bitcoin\u0026rsquo;s safe haven properties through three supervised learning techniques: Logistic Regression, Random Forest, and Extreme Gradient Boosting (XGBoost). Each of these methods has distinct advantages in terms of interpretability, handling nonlinearity, and optimization. Ultimately, we selected XGBoost for its ability to efficiently model \u0026lsquo;tabular data\u0026rsquo; with diverse feature types, its capability to identify nonlinear interactions, and its lower need for strict parameter selection. This makes it more resilient to issues like multicollinearity and class imbalance, which frequently occur in financial time series. In contrast to threshold models like Markov switching or quantile regression that require users to specify regimes and can be unstable with high noise, XGBoost adeptly adapts to structural changes and fluctuations over time. Furthermore, the performance benefits of applying XGBoost in finance have been thoroughly documented (Ji et al., \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Umar et al., \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e\u003cdiv id=\"Sec17\" class=\"Section3\"\u003e\u003ch2\u003e3.4.1 Logistic Regression (LR) - interpretable baseline:\u003c/h2\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{l}\\text{o}\\text{g}\\left(\\frac{P\\left({Y}_{t}=1\\right)}{1-P\\left({Y}_{t}=1\\right)}\\right)={{\\beta\\:}}_{0}+{\\sum\\:}_{i=1}^{k}{{\\beta\\:}}_{i}{X}_{i,t}\\)\u003c/span\u003e\u003c/span\u003e -------(5)\u003c/p\u003e\u003cp\u003eLogistic regression (Eq.\u0026nbsp;5) provides a straightforward and effective baseline, allowing for clear interpretation of coefficients and accurate comparisons with more complex models (Bouri et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2019\u003c/span\u003e).\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec18\" class=\"Section3\"\u003e\u003ch2\u003e3.4.2 Random Forest (RF) \u0026ndash; an ensemble of de-correlated decision trees:\u003c/h2\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\widehat{{Y}_{t}}=\\text{mode}\\left\\{{T}_{1}\\left({X}_{t}\\right),{T}_{2}\\left({X}_{t}\\right),\\dots\\:,{T}_{B}\\left({X}_{t}\\right)\\right\\}\\)\u003c/span\u003e\u003c/span\u003e-------(6)\u003c/p\u003e\u003cp\u003eRandom Forests (as detailed in Eq.\u0026nbsp;6) capture nonlinear relationships among variables by employing bootstrap aggregation and introducing random feature variation. This approach results in robust models that mitigate the risk of overfitting (Šestanović \u0026amp; Kalinić Milićević, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec19\" class=\"Section3\"\u003e\u003ch2\u003e3.4.3 Extreme Gradient Boosting (XGBoost) \u0026ndash; optimized additive model:\u003c/h2\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:{\\mathcal{L}}^{\\left(\\mathcal{t}\\right)}={\\sum\\:}_{i=1}^{n}l\\left({y}_{i},{\\widehat{y}}_{i}^{\\left(t-1\\right)}+{f}_{t}\\left({x}_{i}\\right)\\right)+{\\Omega\\:}\\left({f}_{t}\\right)\\)\u003c/span\u003e\u003c/span\u003e-------(7)\u003c/p\u003e\u003cp\u003ewhere \u003cem\u003efₜ(x\u003csub\u003ei\u003c/sub\u003e)\u003c/em\u003e represents the tree introduced in iteration \u003cem\u003et\u003c/em\u003e, and \u003cem\u003eΩ\u003c/em\u003e serves to regularize complexity. XGBoost (using Eq.\u0026nbsp;7) demonstrates strong performance on structured datasets and exhibits resilience against class imbalance (Ji et al., \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Li \u0026amp; Dai, \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). To address the skewed safe haven, class weighting was incorporated into model training to mitigate bias toward the majority class (Umar et al., \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eAll models were developed in Python with \u003cem\u003escikit-learn\u003c/em\u003e, \u003cem\u003exgboost\u003c/em\u003e, and \u003cem\u003eshap\u003c/em\u003e for modeling and explainability. The benchmark model employed Logistic Regression, while Random Forest was chosen to capture nonlinear relationships. XGBoost was utilized for its scalability and firm performance in financial classification tasks.\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Sec20\" class=\"Section2\"\u003e\u003ch2\u003e3.5 Model Interpretability using SHAP\u003c/h2\u003e\u003cp\u003eIn order to achieve transparent AI and encourage economic explanation, we adopted(using Eq.\u0026nbsp;8) SHAP (SHapley Additive explanations) to measure feature contributions globally and locally. The SHAP explanation model is defined as:\u003c/p\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:f\\left(x\\right)={{\\upvarphi\\:}}_{0}+{\\sum\\:}_{i=1}^{M}{{\\upvarphi\\:}}_{i}\\)\u003c/span\u003e\u003c/span\u003e -------(8)\u003c/p\u003e\u003cp\u003eWhere \u003cem\u003eϕ\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e is the model\u0026rsquo;s expected output, and \u003cem\u003eϕ\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e denotes the marginal contribution of feature \u003cem\u003ei\u003c/em\u003e to the prediction, for instance, \u003cem\u003ex\u003c/em\u003e. SHAP values fulfill essential interpretability properties, including local accuracy, consistency, and robustness to missingness.\u003c/p\u003e\u003cp\u003eTo assess the overall significance of features, global SHAP values were determined by averaging the absolute SHAP values from the test set. This method ensures that the model\u0026rsquo;s interpretation aligns with its performance on unseen data, rather than merely mirroring its behavior during training.\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eSHAP Summary Plots revealed that the divergence indicators between Bitcoin-Gold and Bitcoin-SPX were the strongest influencers of the model\u0026rsquo;s predictions.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eSHAP Force Plots provided explanations tailored to individual instances for the safe haven designations observed during market stress situations.\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003eThe use of SHAP significantly enhances explainable AI (XAI) in the context of modeling high-stakes financial markets, boosting overall interpretability and clarity in decision-making. In addition to providing model explainability, SHAP offers prescriptive decision support. For example, by highlighting divergence spreads or macroeconomic factors, institutional analysts can pinpoint which signals are most influential in safe-haven behavior during times of stress. A notable SHAP value for the bitcoin\u0026ndash;SPX 500 divergence ratio, for instance, would support increasing crypto exposure in risk-off situations. This importantly links AI-derived insights with actionable investment strategies.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec21\" class=\"Section2\"\u003e\u003ch2\u003e3.6 Model Evaluation Metrics\u003c/h2\u003e\u003cp\u003eTo evaluate performance in line with actual market conditions, we implemented an 80/20 stratified train-test split to preserve the relative class distribution of the binary safe haven flag (Yₜ \u0026isin; {0, 1}). Given that financial time series exhibit non-stationarity and dependencies, we chose the 80/20 stratified train-test split over \u003cem\u003ek-fold cross-validation\u003c/em\u003e. Using \u003cem\u003ek-fold cross-validation\u003c/em\u003e could lead to parameters that inaccurately estimate performance or skew performance metrics due to data pooling across folds, especially with an imbalanced dataset.\u003c/p\u003e\u003cp\u003eThe evaluation of model performance utilized the following standard classification metrics:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eAccuracy\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003ePrecision\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eRecall\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eF1 Score\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eReceiver Operating Characteristic Area Under the Curve (ROC-AUC)\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003eThese are defined as\u003c/p\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\text{Accuracy}=\\frac{TP+TN}{TP+TN+FP+FN}\\)\u003c/span\u003e\u003c/span\u003e-------(9)\u003c/p\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{Precision}=\\frac{TP}{TP+FP}\\)\u003c/span\u003e\u003c/span\u003e -------(10)\u003c/p\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\text{Recall}=\\frac{TP}{TP+FN}\\)\u003c/span\u003e\u003c/span\u003e-------(11)\u003c/p\u003e\u003cp\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"429\" height=\"56\"\u003e\u003c/p\u003e\u003cp\u003eROC - AUC\u0026thinsp;=\u0026thinsp;Area under the Receiver Operating Characteristic curve -------(13)\u003c/p\u003e\u003cp\u003eThese performance metrics offer a comprehensive view of model efficacy, particularly when class imbalance can obscure accuracy (Shahzad et al., \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Umar et al., \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). The F1 score effectively balances false positives against false negatives, whereas the ROC-AUC highlights the model\u0026rsquo;s proficiency in distinguishing between thresholds.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec22\" class=\"Section2\"\u003e\u003ch2\u003e3.7 Model Validation Results and Theoretical Significance\u003c/h2\u003e\u003cp\u003eOur framework evaluates both statistical accuracy and the model\u0026rsquo;s capacity to accurately identify divergence related to safe haven events, as outlined in Section \u003cspan refid=\"Sec3\" class=\"InternalRef\"\u003e2.1\u003c/span\u003e. In this regard, recall is especially vital. If a model fails to recognize a genuine safe haven event, it may result in suboptimal capital allocation decisions amid macro-policy stress. Likewise, precision is essential to avoid issuing false safety signals.\u003c/p\u003e\u003cp\u003eXGBoost excelled in F1 and AUC metrics compared to logistic regression and random forest across all models, demonstrating its strong robustness and effectiveness in capturing the nonlinear, conditional aspects of Bitcoin\u0026rsquo;s safe-haven properties.\u003c/p\u003e\u003cp\u003eThis method of classification and evaluation directs our focus towards the idea that divergence-based patterns, informed by macro factors, can be systematically and transparently modeled to highlight Bitcoin\u0026rsquo;s sporadic but significant role as a safe haven.\u003c/p\u003e\u003c/div\u003e"},{"header":"4. Results and Discussions","content":"\u003cdiv id=\"Sec24\" class=\"Section2\"\u003e\u003ch2\u003e4.1.1 Descriptive Statistics\u003c/h2\u003e\u003cp\u003eThis study analyzes daily data from January 1, 2020, to March 31, 2025, encompassing 1,876 observations across three major asset classes: Bitcoin, Gold, and the S\u0026amp;P 500. In addition to core asset returns, we incorporated various macroeconomic indicators, including the VIX Index, CPI, and the FED FUNDS rate. Furthermore, we developed several features focusing on factors such as directional return divergence, relative strength, and lagged macroeconomic conditions that affect safe-haven attributes.\u003c/p\u003e\u003cp\u003eTo assess safe-haven behavior systematically, we created a binary classification rule: A day is designated as a safe-haven event (\u003cem\u003esafe_haven\u0026thinsp;=\u0026thinsp;1\u003c/em\u003e) if Bitcoin has a positive return while both Gold and the S\u0026amp;P 500 report negative returns. This framework captures the conditional migration to Bitcoin during potential stress periods in other asset classes. As shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e above, less than one in seven trading days qualified under this classification, amounting to just 13.11%. This finding implies that safe-haven episodes are sporadic, which is consistent with the research of Bouri et al. (\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) and Corbet et al. (\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eDistribution of Safe Haven vs Non-Safe Haven Days\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"3\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003esafe_haven\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eCount\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e%\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0 (No)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1630\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e86.89\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1 (Yes)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e246\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e13.11\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e presents examples of these episodes, particularly highlighting the timing from March to April 2020, when widespread panic due to COVID-19 appeared to induce significant market dislocations. Bitcoin\u0026rsquo;s divergence during these instances suggests a degree of decoupling from broader systemic selloffs.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eSample Days When Bitcoin acted as a Safe-Haven based on Divergence Logic\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"5\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eDate\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eBitcoin_logret\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eGold_logret\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eSP500_logret\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003esafe_haven\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e14-01-2020\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.068677\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e-0.001246\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e-0.001516\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e31-03-2020\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.002081\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e-0.031872\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e-0.016142\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e21-04-2020\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.003873\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e-0.004263\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e-0.031155\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e28-04-2020\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.003813\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e-0.003913\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e-0.005256\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e06-05-2020\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.032758\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e-0.011993\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e-0.007004\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003ctfoot\u003e\u003ctr\u003e\u003ctd colspan=\"5\"\u003e\u003cem\u003eNote: Log returns are presented in decimal format. For example, 0.01 corresponds to a 1% daily return.\u003c/em\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tfoot\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eTo analyze the statistical behavior of divergence indicators, we present descriptive statistics on the clipped ratios of Bitcoin against Gold and the S\u0026amp;P 500 (Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). Both the \u003cem\u003ebtc_gold_ratio_clipped\u003c/em\u003e and the \u003cem\u003ebtc_sp500_ratio_clipped\u003c/em\u003e exhibit high kurtosis values (16.12 and 11.73, respectively), suggesting the presence of fat tails and significant divergence events. The negative skewness in both indicators indicates that upside divergence (i.e., positive divergence of Bitcoin under stress) is more pronounced than downside convergence.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eDescriptive Statistics of Clipped Divergence Ratios between Bitcoin and Traditional Assets\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"11\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eVariable\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eCount\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eMean\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eStd\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eMin\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003e25%\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e\u003cp\u003e50%\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c8\"\u003e\u003cp\u003e75%\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c9\"\u003e\u003cp\u003eMax\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c10\"\u003e\u003cp\u003eSkewness\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c11\"\u003e\u003cp\u003eKurtosis\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ebtc_gold_ratio_clipped\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1288\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.08\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1.80\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e-10.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e-0.22\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.05\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.36\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\u003cp\u003e10.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e\u003cp\u003e-0.25\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e\u003cp\u003e16.12\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ebtc_sp500_ratio_clipped\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1288\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.03\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2.14\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e-10.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e-0.14\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.11\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.48\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\u003cp\u003e10.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e\u003cp\u003e-1.71\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e\u003cp\u003e11.73\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e analyzes the strength and nature of the relationship between divergence indicators and the \u003cem\u003esafe_haven\u003c/em\u003e flag through Pearson and Spearman correlation coefficients. Although the correlations were weak (ranging from \u0026minus;\u0026thinsp;0.18 to -0.27), they showed consistent directional trends and were statistically significant. Notably, the Spearman values reinforce the idea of a nonlinear, threshold-dependent relationship between divergence and safe-haven classification.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eCorrelation of Divergence Indicators with Safe Haven Flag\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"3\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eDivergence Indicator\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003ePearson Correlation\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eSpearman Correlation\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ebtc_gold_ratio_clipped\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e-0.1837\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e-0.2766\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ebtc_sp500_ratio_clipped\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e-0.1858\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e-0.2742\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eFigure \u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e presents a correlation heatmap of significant returns and macro variables. As anticipated, Bitcoin exhibits a weak correlation with both Gold and the S\u0026amp;P 500. Additionally, macro variables like CPI and FEDFUNDS reveal only minor correlations with Bitcoin, further supporting Kristoufek\u0026rsquo;s (\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) conclusions about Bitcoin\u0026rsquo;s detachment from traditional economic influences. Interestingly, the VIX exhibits a slight correlation with Bitcoin returns, suggesting that behavioral reactions to volatility may be a more significant factor in driving Bitcoin returns than changes in macroeconomic policy.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThese descriptive analytics support the paper\u0026rsquo;s modeling strategy: Bitcoin\u0026rsquo;s safe-haven characteristic is dependent, sporadic, and based on divergences; it is neither consistent nor can it be accounted for through standard or stable correlations with macroeconomic variables.\u003c/p\u003e\u003cp\u003eFigure \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e illustrates the distribution of daily log returns for Bitcoin, Gold, and the S\u0026amp;P 500. The return distribution of Bitcoin is noticeably leptokurtic, featuring heavier tails, which highlights its high volatility and capacity for extreme fluctuations compared to traditional assets. This finding reinforces the view of Bitcoin as a high-risk investment, particularly given its tendency to experience sudden and abrupt price fluctuations. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e illustrates Bitcoin\u0026rsquo;s 30-day rolling volatility, emphasizing notable levels of persistent volatility clustering, particularly during times of macroeconomic shocks and broad intraday market declines. This reinforces the notion that Bitcoin\u0026rsquo;s volatility is a significant characteristic (e.g., \u003cem\u003ebtc_vol_30d\u003c/em\u003e) in the predictive modeling framework, particularly given Bitcoin\u0026rsquo;s distinctive extreme volatility clustering style, as mentioned in Gkillas and Katsiampa (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e illustrates the seasonal analysis of log returns for Bitcoin, Gold, and the S\u0026amp;P 500. In comparison, Bitcoin reveals no apparent seasonality or long-term trend; both Gold and the S\u0026amp;P 500 exhibit mild cyclicality. This supports Bitcoin\u0026rsquo;s unique nature and justifies the use of machine learning over traditional time series models.\u003c/p\u003e\u003cp\u003eFigures \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e and \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e illustrate timelines that highlight the divergence in returns of Bitcoin compared to the S\u0026amp;P 500 and Gold, respectively. These figures suggest that Bitcoin can positively diverge from each market on its own, thereby supporting its potential as an asymmetric hedge in times of stress. Figure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e merges both divergence patterns into a timeline, providing a visual depiction of the dual-dissociation logic applied to the safe-haven flag in this study. Additionally, it highlights distinct periods during which Bitcoin showed positive returns while both traditional assets declined, defining the safe-haven behavior that this study adopts.\u003c/p\u003e\u003cdiv id=\"Sec25\" class=\"Section3\"\u003e\u003ch2\u003e4.1.2 Visual Divergence Diagnostics\u003c/h2\u003e\u003cp\u003eWhile the exploratory summaries provided valuable insights, further diagnostics were conducted to analyze the behavior of divergence metrics across safe-haven and non-haven dates.\u003c/p\u003e\u003cp\u003eFigure \u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e illustrates a distinct rightward shift in the distribution of Bitcoin-Gold divergence for safe-haven dates compared to non-haven dates. The density curve for safe-haven days reveals a longer and broader tail, suggesting that Bitcoin often outperforms Gold, especially during market turmoil, and with greater intensity. This reinforces the notion that diverging from traditional assets is a fundamental aspect of Bitcoin\u0026rsquo;s role as a safe-haven asset.\u003c/p\u003e\u003cp\u003eFigure \u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e illustrates the distribution of Bitcoin-S\u0026amp;P 500 divergence values across classifications of safe-haven and non-haven dates. During safe-haven dates, there is a noticeable shift towards higher divergence values, suggesting that Bitcoin often experiences a positive decoupling from equity markets in times of adversity. This trend reinforces Bitcoin\u0026rsquo;s potential as a conditional hedge against declines in equity markets. Figure\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e presents a density plot illustrating divergence, marked by vertical lines that indicate the mean divergence for each class. The data shows that observations of safe-haven exhibit a significantly higher mean divergence compared to non-haven days. This finding supports the notion that Bitcoin decouples more profoundly from the S\u0026amp;P 500 during periods when it is regarded as a safe haven. The distinction in central tendency adds statistical significance to our framework for classifying divergence.\u003c/p\u003e\u003cp\u003eFigure \u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e illustrates the distributions of the log return ratio of Bitcoin compared to the S\u0026amp;P 500, with a focus on its status as a safe haven. The safe-haven category exhibits a longer right tail and peaks further right than the non-haven category, indicating that Bitcoin tends to outperform equities when it serves as a safe haven. This asymmetric deviation from symmetry acknowledges the use of engineered ratio features for modeling purposes. The time-series plot in Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e displays the daily divergence values of Bitcoin from Gold and the S\u0026amp;P 500, with safe-haven events marked in red. There is a consistent correlation between safe-haven events and spikes in divergence values, which supports the temporal validity of the rule-based approach used in identifying safe-haven flags. This further reinforces the rationale for employing divergence logic to describe and model episodic safe-haven behavior in Bitcoin.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec26\" class=\"Section3\"\u003e\u003ch2\u003e4.1.3 Macro-Condition Separation Diagnostics\u003c/h2\u003e\u003cp\u003eThe assessment of CPI levels on both safe-haven and non-haven days revealed a significant overlap between the two categories, indicating that inflation is not the main factor influencing Bitcoin\u0026rsquo;s divergence behavior. This aligns with Kristoufek (\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2015\u003c/span\u003e), who noted Bitcoin\u0026rsquo;s separation from traditional inflation-related assets. As illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e, we depict the distribution of VIX, which indicates equity market volatility. Safe-haven days typically showed markedly right-skewed distributions. While there was still significant overlap, the right skew suggests slightly heightened volatility conditions regarding Bitcoin as a safe haven, reinforcing the hypothesis that instances of safe-haven Bitcoin transactions are generally tied to increased uncertainty, as well as these clustered behaviors in digital assets (Gkillas \u0026amp; Katsiampa, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Figure\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003e shows the distribution of FEDFUNDS across the two classes. The nearly identical distributions suggest that interest rate policy has a minimal direct impact on safe-haven flag classification, further emphasizing what appears to be a nonlinear, event-driven, and largely independent safe-haven response to monetary policy levels.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Sec27\" class=\"Section2\"\u003e\u003ch2\u003e4.2 Modeling Performance\u003c/h2\u003e\u003cp\u003eThis study classifies Bitcoin\u0026rsquo;s role as a conditional safe haven by examining engineered divergence predictors, macroeconomic indicators, and market volatility signals. The dependent variable (\u003cem\u003esafe_haven\u003c/em\u003e) is a binary response, defined through a rule-based label indicating instances when Bitcoin\u0026rsquo;s price rose while both Gold and the S\u0026amp;P 500 fell. We performed three classifications: Logistic regression, Random Forest, and XGBoost, to assess whether traditional linear classifiers, such as Logistic regression, can effectively capture the nonlinear divergence trajectories linked to safe-haven behavior, or if the predictive power of ensemble tree-based methods is superior.\u003c/p\u003e\u003cdiv id=\"Sec28\" class=\"Section3\"\u003e\u003ch2\u003e4.2.1 Classifier Comparison\u003c/h2\u003e\u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e summarizes the model\u0026rsquo;s performance across five key metrics: accuracy, Recall, Precision, F1 Score, and Area Under the receiver operating characteristic curve (AUC). Among the three models, XGBoost initially excelled by effectively identifying rare safe-haven signals and achieving high recall and AUC scores, which led to its selection for further assessment of explainability.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eComparative Performance Summary of Logistic Regression, Random Forest, and XGBoost\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"6\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eModel\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eAccuracy\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eRecall (Class 1)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003ePrecision (Class 1)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eF1 Score\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eROC AUC\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eLogistic Regression\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.79\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.35\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.69\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.46\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.88\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRandom Forest\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.97\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.98\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eXGBoost\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003e0.996\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e\u003cb\u003e0.94\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cb\u003e1\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e\u003cb\u003e0.97\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e\u003cb\u003e0.997\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec29\" class=\"Section3\"\u003e\u003ch2\u003e4.2.2 Confusion Matrix and ROC Curve\u003c/h2\u003e\u003cp\u003eTo assess the classification performance, refer to the confusion matrix of the fitted XGBoost model in Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. Among the 17 safe-haven instances in the testing set, 15 were accurately classified, and the model did not misclassify any additional instances as safe havens. Classification performance metrics are presented in Table\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e7\u003c/span\u003e. Figure\u0026nbsp;\u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e15\u003c/span\u003e illustrates the XGBoost model\u0026rsquo;s proficiency in detecting the minority class, as evidenced by an AUC of 0.997, indicating near-perfect performance. These assessments confirm that XGBoost maintains high sensitivity and overall predictive accuracy, even in the presence of class imbalance.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eConfusion Matrix for XGBoost Predictions on the Test Set\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"3\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003ePredicted: Non-Haven (0)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003ePredicted: Safe Haven (1)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eActual: Non-Haven (0)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e235\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eActual: Safe Haven (1)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e15\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab7\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eClassification Report for XGBoost Predictions on the Test Set\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"5\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eClass\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003ePrecision\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eRecall\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eF1-Score\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eSupport\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eNon-Haven (0)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.99\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e235\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSafe Haven (1)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.88\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.94\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e17\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eAccuracy\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cb\u003e0.99\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e252\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eMacro Average\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.94\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.97\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e252\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eWeighted Average\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.99\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.99\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.99\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e252\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Sec30\" class=\"Section2\"\u003e\u003ch2\u003e4.3 Explainability with SHAP\u003c/h2\u003e\u003cp\u003eWe applied SHAP (SHapley Additive exPlanations) to the fitted XGBoost model to improve transparency and assess the role of each feature in determining the safe haven status of individual observations. SHAP calculates the marginal effect of every input feature for each prediction, providing both global importance rankings and local interpretability (Lundberg \u0026amp; Lee, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). This approach enhances transparency and aligns with contemporary definitions of explainable AI (XAI) by offering a data-driven rationale for the divergence-based features we developed earlier. Additionally, it supports fundamental XAI principles such as accountability and actionability (Doshi-Velez \u0026amp; Kim, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). Figure\u0026nbsp;\u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e16\u003c/span\u003e showcases the global SHAP summary, highlighting that \u003cem\u003ebtc_sp500_ratio\u003c/em\u003e emerged as the most significant feature, followed by \u003cem\u003eSP500_logret, Gold_logret\u003c/em\u003e, and \u003cem\u003ebtc_gold_ratio.\u003c/em\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThis further suggests that Bitcoin\u0026rsquo;s performance during downturns is the main reason it is considered a safe-haven asset. Table\u0026nbsp;\u003cspan refid=\"Tab8\" class=\"InternalRef\"\u003e8\u003c/span\u003e presents data on the top 10 features, ranked by their contribution as indicated by SHAP values. The SHAP beeswarm plot in Fig.\u0026nbsp;\u003cspan refid=\"Fig17\" class=\"InternalRef\"\u003e17\u003c/span\u003e offers more profound insight into directional influence. Elevated \u003cem\u003ebtc_sp500_ratio\u003c/em\u003e values (the red dots to the right) consistently indicate positive SHAP values, enhancing the model\u0026rsquo;s likelihood of predicting a safe haven (flag\u0026thinsp;=\u0026thinsp;1). Conversely, negative values from \u003cem\u003eSP500_logret\u003c/em\u003e and \u003cem\u003eGold_logret\u003c/em\u003e (the blue dots on the left) drive predictions towards flag\u0026thinsp;=\u0026thinsp;0, consistent with the initial rule-based divergence flag logic. This suggests that Bitcoin\u0026rsquo;s rise, occurring alongside declines in equity and Gold, is the key signal the model identifies as significant, as captured through both raw log returns and engineered ratios.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab8\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 8\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eTop 10 Predictive Features Ranked by SHAP Importance\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRank\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eFeature Index\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eFeature\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eMean(|SHAP|)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e26\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003ebtc_sp500_ratio\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2.77\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eSP500_logret\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1.17\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eGold_logret\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1.10\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e25\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003ebtc_gold_ratio\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1.04\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003ebtc_gold_divergence\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.86\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e27\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003ebtc_gold_ratio_clipped\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.64\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003ebtc_sp500_divergence\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.60\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e28\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003ebtc_sp500_ratio_clipped\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.19\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e23\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003ebtc_vs_gold_logret_ratio\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.18\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e24\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003ebtc_vs_sp500_logret_ratio\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.08\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eEach point indicates a single observation, where red denotes high feature values and blue indicates low values. Features such as \u003cem\u003ebtc_sp500_ratio\u003c/em\u003e and \u003cem\u003ebtc_gold_ratio\u003c/em\u003e enhance safe-haven classification, while decreases in \u003cem\u003eSP500_logret\u003c/em\u003e and \u003cem\u003eGold_logret\u003c/em\u003e undermine it, thus supporting the divergence-based logic. Our results align with recent literature, providing initial evidence of nonlinear, episodic behavior in Bitcoin\u0026rsquo;s connection with traditional markets (Bouri et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Yae \u0026amp; Tian, \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Bitcoin does not act as a stable, safe-haven asset with consistent hedging traits; instead, it functions as a conditional hedge that responds to relative return divergences rather than macroeconomic fundamentals, such as the volatility index (VIX) or monetary policy interest rates (FED FUNDS).\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec31\" class=\"Section2\"\u003e\u003ch2\u003e4.4 Comparative Modeling and Interpretation\u003c/h2\u003e\u003cp\u003eTo assess the robustness and generalizability of the divergence-based safe-haven classification, we trained and evaluated three models: Logistic Regression, Random Forest, and XGBoost. All models were trained on the same balanced dataset and tested using stratified holdout and cross-validation methods.\u003c/p\u003e\u003cdiv id=\"Sec32\" class=\"Section3\"\u003e\u003ch2\u003e4.4.1 Logistic Regression: Benchmark Interpretability\u003c/h2\u003e\u003cp\u003eLogistic regression served as the baseline model due to its interpretability and ease of use. The metrics show solid performance for class 0 (non-safe haven) with a precision of 0.99 and an accuracy of 0.88. For class 1 (safe-haven) detection, it achieved a precision of 0.35, a recall of 0.88, and an F1 score of 0.50. The ROC AUC score is robust at 0.95 (Table\u0026nbsp;\u003cspan refid=\"Tab9\" class=\"InternalRef\"\u003e9\u003c/span\u003e), while the mean section cross-validated AUC of 0.9516\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0069 across five folds suggests good generalization stability.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab9\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 9\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eComparative Classification Performance of Models\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"7\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eModel\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eClass\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003ePrecision\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eRecall\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eF1-Score\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eSupport\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e\u003cp\u003eROC AUC\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eLogistic Regression\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.99\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.88\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.93\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e235\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.95\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.35\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.88\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e17\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eMacro Avg\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cb\u003e0.67\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cb\u003e0.88\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e\u003cb\u003e0.72\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e252\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eWeighted Avg\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cb\u003e0.9\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cb\u003e0.88\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e\u003cb\u003e0.89\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e252\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eRandom Forest\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.99\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e235\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.88\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.94\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e17\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eMacro Avg\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cb\u003e1\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cb\u003e0.94\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e\u003cb\u003e0.97\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e252\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eWeighted Avg\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cb\u003e0.99\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cb\u003e0.99\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e\u003cb\u003e0.99\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e252\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eXGBoost\u003c/b\u003e (from earlier phase)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e\u003cb\u003e0.97\u003c/b\u003e (AP from PR curve)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eThis shows that a linear model can still identify nonlinear divergence patterns when the features are well-engineered. However, the lower precision for class 1 suggests that logistic regression may over-predict the safe-haven condition in specific edge cases.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec33\" class=\"Section3\"\u003e\u003ch2\u003e4.4.2 Random Forest: Nonlinear Ensemble Performance\u003c/h2\u003e\u003cp\u003eThe Random Forest classifier greatly exceeded logistic regression, achieving perfect precision and recall scores (1.00) for class 1 and an overall test set accuracy of 0.99. Additionally, the ROC AUC score reflects a flawless classification boundary (1.00). These outcomes highlight the nonlinear and interaction-driven characteristics of safe-haven episodes, which tree-based ensembles can uniquely capture.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec34\" class=\"Section3\"\u003e\u003ch2\u003e4.4.3 Model Comparison via Precision\u0026ndash;Recall Curves\u003c/h2\u003e\u003cp\u003eTo assess model performance under conditions of class imbalance, we generated Precision-Recall (PR) curves for all three models (Fig.\u0026nbsp;\u003cspan refid=\"Fig18\" class=\"InternalRef\"\u003e18\u003c/span\u003e). In summary, XGBoost achieved a commendable average precision (AP) of 0.97, while Random Forest excelled with an AP of 1.00, and Logistic Regression recorded an AP of 0.53. These findings further support the value of ensemble modeling in capturing high-risk divergence behavior and corroborate previous calls for tree-based modeling approaches for cryptocurrency volatility and hedging (Bouri et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Abdalhammed et al., \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Šestanović \u0026amp; Kalinić Milićević, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Additionally, Mallqui and Fernandes (\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) noted that Random Forests were valuable in modeling daily Bitcoin prices.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Sec35\" class=\"Section2\"\u003e\u003ch2\u003e4.5 Robustness Checks and Prescriptive Stratifications\u003c/h2\u003e\u003cdiv id=\"Sec36\" class=\"Section3\"\u003e\u003ch2\u003e4.5.1 Cross-Validation Robustness\u003c/h2\u003e\u003cp\u003eTo evaluate the model\u0026rsquo;s generalizability and prevent overfitting, we conducted a 5-fold cross-validation using the AUC metric on the Random Forest model. The results demonstrated exceptional consistency across the folds, with each fold yielding an AUC of 1.0 and a standard deviation of 0. The outcomes were uniform across all folds, suggesting that the model's structure and the dependent relationships among features should remain reliably accurate across different partitions of the dataset. This conclusion aligns with the prevalence of similar features across combinations in the SHAP analysis and is consistent with the validation results from the original dataset of the XGBoost model.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec37\" class=\"Section3\"\u003e\u003ch2\u003e4.5.2 Prescriptive Stratification for Decision Support\u003c/h2\u003e\u003cp\u003eTransitioning from binary classification, the model\u0026rsquo;s probabilistic output has been segmented into three confidence areas (representing three actionable decisions probabilistically):\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eHigh Certainty Safe-haven (P\u0026thinsp;\u0026ge;\u0026thinsp;0.8)\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eModerate Certainty (0.5\u0026thinsp;\u0026le;\u0026thinsp;P\u0026thinsp;\u0026lt;\u0026thinsp;0.8)\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eLow Certainty / No Signal (P\u0026thinsp;\u0026lt;\u0026thinsp;0.5)\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003eBased on these thresholds, the majority of predictions (237 out of 252) remained in the low-certainty zone, with 15 confidently marked as safe-haven cases. Figure\u0026nbsp;\u003cspan refid=\"Fig19\" class=\"InternalRef\"\u003e19\u003c/span\u003e displays this classification, emphasizing the episodic and rare instances of Bitcoin\u0026rsquo;s safe-haven signals. This probability classification offers a more practical and understandable approach for portfolio managers; we not only deliver binary outputs but also convey a level of confidence in those results.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec38\" class=\"Section3\"\u003e\u003ch2\u003e4.5.3 Threshold-Specific Precision\u0026ndash;Recall Analysis\u003c/h2\u003e\u003cp\u003eThe analysis of the model\u0026rsquo;s output focused on prescriptive performance by examining rates starting at the minimum threshold of 0.3 and evaluating higher thresholds up to 0.9. As shown in Table\u0026nbsp;\u003cspan refid=\"Tab10\" class=\"InternalRef\"\u003e10\u003c/span\u003e, precision was flawless (1.00) across all thresholds, while recall improved with decreasing thresholds. Specifically, a threshold of 0.3 yielded the highest recall (0.94) and an F1 score, representing a balance between confidence and sensitivity, of 0.97. Therefore, these isolated results instill confidence in the model\u0026rsquo;s reliability in scenarios where failing to identify safe-haven signals incurs significantly higher costs than false alarms, as previously mentioned in crises (Kristoufek, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Corbet et al., \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab10\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 10\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eThreshold-Specific Evaluation Metrics for Safe Haven Classification (Random Forest)\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"8\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eThreshold\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eTP\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eFP\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eTN\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eFN\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003ePrecision\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e\u003cp\u003eRecall\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c8\"\u003e\u003cp\u003eF1 Score\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e14\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e235\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.82\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.9\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e15\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e235\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.88\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.94\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e15\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e235\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.88\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.94\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e15\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e235\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.88\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.94\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e15\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e235\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.88\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.94\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e15\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e235\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.88\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.94\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e16\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e235\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.94\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.97\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e"},{"header":"5. Conclusion","content":"\u003cp\u003eThis study presents a divergence-based, explainable machine-learning framework for assessing Bitcoin\u0026rsquo;s function as a conditional safe-haven asset. By developing a rule-based classification flag that identifies instances when Bitcoin rises while both Gold and the S\u0026amp;P 500 decline, we provide a replicable and data-driven method for capturing flight-to-safety behavior during macro-financial stress. Empirical results reveal that XGBoost consistently surpasses both logistic regression and random forest in identifying these episodic safe haven occurrences. The implementation of SHAP (SHapley Additive exPlanations) enables the transparent interpretation of model predictions, highlighting that Bitcoin\u0026rsquo;s divergence from traditional asset returns is the primary factor influencing safe-haven behavior. These findings support the idea that Bitcoin\u0026rsquo;s hedge-like behavior is not constant but instead conditional and influenced by stress. In addition to accuracy, the integration of SHAP interpretability and probabilistic classification zones enhances the model\u0026rsquo;s prescriptive relevance. This facilitates practical application in institutional environments, especially for those pursuing regulatory-compliant AI models and decision-support systems to navigate financial uncertainty.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eConflict of interest\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDeclaration of generative AI and AI-assisted technologies in the writing process\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eDuring the preparation of this work, the author used Grammarly and Litmaps to check the English grammar and logical framework and extesnive liteature review. After using this tool/service, the author reviewed and edited the content as needed and took full responsibility for the content of the publication.\u003c/p\u003e\u003cp\u003e\u003ch2\u003eEthics Declaration\u003c/h2\u003e\u003cp\u003eThis study did not involve human participants, personal data, or confidential information. Therefore, ethical approval was not required.\u003c/p\u003e\u003ch2\u003eFunding\u003c/h2\u003e\u003cp\u003eThis research received \u003cb\u003eno specific grant\u003c/b\u003e from any funding agency in the public, commercial, or not-for-profit sectors.\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eM.B.R. conceptualized the research design, conducted the imputation benchmarking experiments, and performed the SHAP-based interpretability analysis. M.B.R. also wrote the main manuscript text, curated all figures and tables, and ensured methodological rigor through statistical testing. All authors reviewed and approved the final manuscript.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAbdalhammed, M. K., Ghazal, A. M., Ibrahim, H. M., \u0026amp; Ahmed, A. K. (2022). Application deep learning to predict cryptocurrency prices and their relationship to market adequacy (Applied research Bitcoin as an example). Finance: Theory and Practice, 26(4), 95\u0026ndash;108. https://doi.org/10.26794/2587-5671-2022-26-4-95-108\u003c/li\u003e\n\u003cli\u003eAljinović, Z., \u0026Scaron;estanović, T., \u0026amp; \u0026Scaron;krabić Perić, B. (2022). A new evidence of the relationship between cryptocurrencies and other assets from the COVID-19 crisis. Journal of Economics / Ekonomicky casopis, 70(7\u0026ndash;8), 603\u0026ndash;621. https://doi.org/10.31577/ekoncas.2022.07-8.03\u003c/li\u003e\n\u003cli\u003eAtsalakis, G. S., Atsalaki, I. G., Pasiouras, F., \u0026amp; Zopounidis, C. (2019). Bitcoin price forecasting with neuro-fuzzy techniques. 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Finance Research Letters, 16, 85\u0026ndash;92. https://doi.org/10.1016/j.frl.2015.10.008\u003c/li\u003e\n\u003cli\u003eFawaz, H. I., Forestier, G., Weber, J., Idoumghar, L., \u0026amp; Muller, P. A. (2019). Deep learning for time series classification: A review. Data Mining and Knowledge Discovery, 33, 917\u0026ndash;963. https://doi.org/10.1007/s10618-019-00619-1\u003c/li\u003e\n\u003cli\u003eGandal, N., Hamrick, J., Moore, T., \u0026amp; Oberman, T. (2018). Price manipulation in the Bitcoin ecosystem. Journal of Monetary Economics, 95, 86\u0026ndash;96. https://doi.org/10.1016/j.jmoneco.2017.12.004\u003c/li\u003e\n\u003cli\u003eGkillas, K., \u0026amp; Katsiampa, P. (2018). An application of extreme value theory to cryptocurrencies. Economics Letters, 164, 109\u0026ndash;111. https://doi.org/10.1016/j.econlet.2018.01.020\u003c/li\u003e\n\u003cli\u003eGriffin, J. M., \u0026amp; Shams, A. (2020). Is Bitcoin really un-tethered? 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Retrieved from https://eudoxuspress.com/index.php/pub/article/view/2762\u003c/li\u003e\n\u003cli\u003eShen, Z., Wan, Q., \u0026amp; Leatham, D. J. (2021). Bitcoin return volatility forecasting: A comparative study between GARCH and RNN. Journal of Risk and Financial Management, 14(7), 337. https://doi.org/10.3390/jrfm14070337\u003c/li\u003e\n\u003cli\u003eTodorovska, A., Peshov, H., Rusevski, I., Vodenska, I., Chitkushev, L. T., \u0026amp; Trajanov, D. (2023). Using ML and explainable AI to understand the interdependency networks between classical economic indicators and crypto-markets. Physica A: Statistical Mechanics and Its Applications, 624, 128900. https://doi.org/10.1016/j.physa.2023.128900\u003c/li\u003e\n\u003cli\u003eUmar, M., Su, C.-W., Rizvi, S. K. A., \u0026amp; Shao, X.-F. (2021). Bitcoin: A safe haven asset and a winner amid political and economic uncertainties in the US? Technological Forecasting and Social Change, 167, 120680. https://doi.org/10.1016/j.techfore.2021.120680\u003c/li\u003e\n\u003cli\u003eYae, J., \u0026amp; Tian, G. Z. (2024). Volatile safe-haven asset: Evidence from Bitcoin. Journal of Financial Stability, 73, 101285. https://doi.org/10.1016/j.jfs.2024.101285\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Divergence modeling, Explainable AI, Logistic Regression, XGBoost, SHAP","lastPublishedDoi":"10.21203/rs.3.rs-6909016/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6909016/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study examines the role of Bitcoin as a potential safe haven during periods of macroeconomic stress caused by US policy shocks. Utilizing daily data from January 2020 to March 2025, including Bitcoin, Gold, the S\u0026amp;P 500, VIX, CPI, and the Federal Funds Rate, we create an innovative divergence-based framework. Bitcoin qualifies as a safe haven only when it appreciates while both Gold and the S\u0026amp;P 500 decline, reflecting flight-to-safety behavior. An XGBoost classifier, trained on engineered divergence and macro-financial features, significantly outperforms Random Forest and Logistic Regression, achieving an AUC of 0.997 and a recall rate of 0.88. SHAP-based explainability indicates that Bitcoin\u0026rsquo;s return divergence from traditional assets is the most significant predictor of its safe-haven behavior. The results confirm that Bitcoin does not consistently act as a hedge but exhibits episodic, stress-driven, safe-haven characteristics. This framework enhances the understanding of Bitcoin\u0026rsquo;s behavior in response to systemic shocks, providing transparent, data-driven decision support for investors facing financial uncertainty.\u003c/p\u003e","manuscriptTitle":"Classifying Bitcoin’s Safe Haven Role Using Explainable AI: Evidence from US Macroeconomic Stress Episodes","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-07-15 10:30:23","doi":"10.21203/rs.3.rs-6909016/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"c5a2058d-615e-4791-906a-ecbe64d65a5b","owner":[],"postedDate":"July 15th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-10-27T16:25:48+00:00","versionOfRecord":{"articleIdentity":"rs-6909016","link":"https://doi.org/10.1007/s11135-025-02424-z","journal":{"identity":"quality-and-quantity","isVorOnly":false,"title":"Quality \u0026 Quantity"},"publishedOn":"2025-10-25 16:16:23","publishedOnDateReadable":"October 25th, 2025"},"versionCreatedAt":"2025-07-15 10:30:23","video":"","vorDoi":"10.1007/s11135-025-02424-z","vorDoiUrl":"https://doi.org/10.1007/s11135-025-02424-z","workflowStages":[]},"version":"v1","identity":"rs-6909016","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6909016","identity":"rs-6909016","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}