Designing an efficient Deep Dyna Q based VARMAx Model for Prediction of Real-Time changes in Stock Value Patterns

Designing an efficient Deep Dyna Q based VARMAx Model for Prediction of Real-Time changes in Stock Value Patterns | 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 Designing an efficient Deep Dyna Q based VARMAx Model for Prediction of Real-Time changes in Stock Value Patterns Rachna Sable, Aman Singh, Sudhanshu Gupta, Pallavi Parlewar This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5794220/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract In the intricate complexities of modern financial markets, the capability to predict stock values with high accuracy stands as a cornerstone for investors and analysts alike. Existing methods still struggle with the complex dynamics of markets, especially in adapting to stock fluctuations' multifaceted nature. In response to these limitations, the proposed work introduces a ground-breaking approach that integrates the robust forecasting capabilities of VARMAx with the adaptive ability of Deep Dyna Q algorithms. The rationale for this integration is rooted in the quest to enhance the responsiveness and accuracy of stock value predictions. The model's performance was evaluated using datasets from the Indian and USA markets. It showed significant improvements in precision, accuracy, recall, AUC, and specificity, as well as a substantial reduction in response time. These enhancements are crucial for financial decision-making, where accuracy and timeliness are essential. Deep Dyna Q VARMAx Stock Market Prediction Financial Analytics Hyperparameter Tuning Scenarios Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 1 Introduction The introduction of computational techniques in finance has marked a significant shift from traditional methods, offering a more nuanced understanding of market dynamics. However, despite the advancements, existing models often struggle to keep pace with the rapidly evolving and complex nature of stock markets. This gap underscores a critical need for more sophisticated, adaptive models that can effectively interpret and predict real-time changes in stock values. The introduction of Vector Autoregressive Moving Average with eXogenous inputs (VARMAx) models marked significant progress by incorporating external factors and historical data to capture complex interactions in financial markets. However, their static hyperparameters pose a limitation, as they cannot adapt to changing market conditions, leading to potentially suboptimal predictions. To address this, the current work integrates the robust forecasting capabilities of VARMAx with the adaptive power of Deep Dyna Q algorithms. This integration enhances stock value predictions' responsiveness and accuracy by using Deep Dyna Q, a reinforcement learning algorithm, to continuously adjust VARMAx hyperparameters in real-time, accommodating various stock types and market conditions. In conclusion, this introduction sets the stage for a detailed exploration of the proposed model, its methodological framework, the rationale behind its design, and its impactful contributions to the field of financial analytics. The subsequent sections will delve deeper into the technical aspects of the model, the nuances of its implementation, and a comprehensive analysis of its performance, thereby unfolding the full narrative of this innovative approach to stock value predictions. 2 Literature review As shown through various research studies, the recent advancements in stock price prediction methodologies underscore the significant strides made in financial technology. This literature review synthesizes insights from fifteen notable studies, each contributing uniquely to the understanding of stock market dynamics and predictive analytics. An innovative method for stock price prediction using a combination of BiLSTM and an improved transformer model was developed by [ 1 ]. This approach highlighted the efficacy of integrating deep learning techniques for financial forecasting. Similarly, work by [ 2 ] emphasized the role of investor sentiment in stock price prediction, utilizing optimized deep learning methods to enhance prediction accuracy. These studies collectively underscore the growing reliance on complex algorithms in financial market analysis. The work by [ 3 ] introduced a Cost Harmonization LightGBM-based model for stock market prediction, highlighting a novel approach in utilizing gradient boosting frameworks. The work by [ 4 ] advanced this discussion by illustrating the use of Graph Evolution Recurrent Unit for learning dynamic dependencies in stock predictions, emphasizing the importance of understanding temporal relationships in financial data samples. [ 5 ] investigated hierarchical adaptive temporal relational interaction using their HATR-I model to forecast stock trends, emphasising the importance of relational and temporal dynamics in market analysis. [ 6 ] proposed a Hybrid Information Mixing Module for stock movement prediction, thereby stressing the integration of diverse data sources for improved accuracy. [ 7 ] proposed a unique ensemble learning strategy for stock market prediction that combines sentiment analysis and the sliding window method. This study demonstrated the increased importance on sentiment analysis in financial forecasting. [ 8 ] focused on the Signature Transform of Limit Order Book Data for stock price prediction, highlighting the potential of order book data in predictive analysis. [ 9 ] discussed the Transformer-Gated Recurrent Unit Method for predicting stock prices based on news sentiments and technical indicators. This approach emphasized the multifaceted nature of stock market prediction, where various external and internal factors were considered. [ 10 ] provided a comprehensive view of artificial intelligence applications in the economy, including stock trading and market analysis, underlining the broader context of AI in financial decision-making.[ 11 ] explored the realm of reinforcement learning for stock prediction, specifically addressing high-frequency trading with T + 1 rules. This study exemplifies the application of reinforcement learning in a practical trading context. [ 12 ] focused on the exploitation of macroeconomic indicators for stock direction classification, using the Multimodal Fusion Transformer to integrate diverse economic indicators into predictive models.[ 13 ] delve into adversarial learning networks for FinTech applications using heterogeneous data sources, suggesting the potential of adversarial networks in handling diverse financial data samples. [ 14 ] introduced FinGAT, a financial graph attention network for recommending profitable stocks, highlighting the use of attention mechanisms in stock selection. [ 15 ] explored the application of offline reinforcement learning in automated stock trading. This study represented a critical step forward in the application of reinforcement learning techniques, particularly in the context of environments where real-time interaction is not feasible. [ 16 ] presented a hybrid CNN-LSTM model for portfolio performance, focusing on stock selection and optimization. This model exemplifies the effective combination of convolutional and recurrent neural networks in financial applications, offering insights into the utility of deep learning architectures in stock market analytics. [ 17 ] delve into an evolutionary trading signal prediction model, optimized based on Chinese news and technical indicators within the Internet of Things framework. This study underscores the significance of integrating diverse data sources, including news sentiment, for enhancing predictive accuracy in trading models. [ 18 ] contributed to the field by enhancing stock portfolios for enterprise management and investment, specifically in the energy industry. Their work illustrated the sector-specific application of stock market predictions, emphasizing the contextual adaptation of predictive models. [ 19 ] proposed a medium to long-term multi-influencing factor copper price prediction method utilizing a CNN-LSTM network. This approach is notable for its application to commodity price prediction, extending the scope of predictive analytics beyond traditional stock prices. [ 20 ] introduced a two-stage portfolio optimization integrating an optimal sharp ratio measure and ensemble learning. This study is pivotal in illustrating the application of ensemble methods in optimizing financial portfolios, emphasizing the balance between risk and return. [ 21 ] discussed a portfolio selection strategy based on peak price involving randomness. This approach adds to the understanding of stochastic elements in financial decision-making. [ 22 ] provided a systematic survey of AI models in financial market forecasting for profitability analysis. Their comprehensive review offered a broad perspective on the various methodologies and their effectiveness in financial forecasting. [ 23 ] discussed a synthetic feature processing method for remaining useful life prediction of rolling bearings. While distinct from stock market prediction, this study highlights the broader applicability of predictive models in different domains of reliability engineering. Finally, [ 24 ] enhanced time series predictors with a generalized extreme value loss. This advancement in loss function optimization has implications for improving the accuracy and robustness of predictive models in time series analysis. [ 25 ] proposed a bi-directional long short-term memory (Bi-LSTM) model for predicting future stock prices based on historical data. Unlike standard LSTM, Bi-LSTM captures both short- and long-term dependencies by processing sequences forward and backward. Applied to Apple's stock price data, the model's performance was evaluated using mean squared error (MSE) and visual comparison of actual vs. predicted prices. The experiments showed Bi-LSTM makes accurate predictions and captures trends, though it may struggle with sudden market changes. Overall, it was concluded that Bi-LSTM is a promising tool for stock price prediction with many potential applications in finance. A hybrid modeling approach for stock price prediction, combining machine learning and deep learning models was proposed by [ 26 ]. Using NIFTY 50 index dataset a regression model was used to predict open values. The framework was then enhanced with four deep learning-based regression models using LSTM networks and walk-forward validation. Optimized through grid-searching, the LSTM models ensured stable validation losses and accuracy convergence. Results showed that LSTM univariate model, using one-week prior data for next week's prediction, is the most accurate. The work in [ 27 ] used deep learning to predict one-month-ahead stock returns in the Japanese market and evaluates its performance. Results showed that deep neural networks outperform shallow networks and other machine learning models, indicating deep learning's potential for predicting stock returns. The effectiveness of stock price and return as input features in directional forecasting models using 10-year historical data from ten large-cap US companies were compared by [ 28 ]. Employing four popular classification algorithms, the analysis showed that stock price is a more effective standalone input than return. However, their effectiveness equalizes when technical indicators are included. It was concluded that stock price generally outperforms return in predicting price direction, offering valuable insights for researchers and practitioners in stock price forecasting. These studies collectively demonstrate a trend towards more sophisticated, data-driven approaches in stock trading and portfolio management. They emphasize the role of machine learning, particularly deep learning, reinforcement learning, and ensemble methods, in decoding complex market dynamics. The integration of diverse data sources, including news sentiment and technical indicators, further enriches the predictive capabilities of these models. This body of work advances financial technology and provides valuable insights for practitioners and researchers in developing more effective and efficient predictive models for financial markets. In summary, the literature in ML-based stock market analysis reflects a trajectory of increasing sophistication and complexity, moving from simple linear models to advanced neural networks and adaptive learning algorithms. Each stage in this evolution has contributed to a deeper understanding and more accurate prediction of stock market behavior, culminating in the current trend of integrating diverse data sources and employing adaptive algorithms for real-time analysis. Motivation & Contributions The literature indicates that traditional forecasting models, though foundational, often fail to capture the complex and dynamic nature of the stock market. This limitation is especially pronounced during periods of market volatility, where rapid changes require a predictive model that is both accurate and adaptable in real-time. The inability of these models to adjust to varying market conditions highlights the need for a more advanced approach that can intelligently evolve with the ever-changing financial landscape. It is in this context that the current study introduces an innovative model, merging the strengths of VARMAx with the adaptive capabilities of Deep Dyna Q algorithms. The VARMAx model's ability to incorporate external factors and historical data presents a solid foundation for understanding market dynamics. However, the static nature of its hyperparameters limits its adaptability. This limitation forms the crux of our motivation: to enhance the VARMAx model with a mechanism that allows for dynamic adjustment and real-time responsiveness. The integration of Deep Dyna Q algorithms addresses this gap. Renowned for their efficacy in environments requiring continuous learning, these algorithms offer a means to dynamically tune hyperparameters, thereby enabling the model to adjust its predictive strategy in response to market fluctuations. This novel approach not only enhances the accuracy of stock value predictions but also significantly reduces the response time, a critical factor in financial markets where opportunities are fleeting. The contributions of this research are multifaceted and substantial. Firstly, it presents a pioneering model that seamlessly blends advanced machine learning techniques with traditional econometric methods, setting a new benchmark in stock market prediction. Secondly, the empirical validation of the model across diverse stock markets, including those of India and the USA, demonstrates its robustness and applicability in varying market conditions. This is evidenced by the model's superior performance metrics, including improved precision, accuracy, recall, AUC, specificity, and reduced delay, compared to existing methods. Moreover, this research contributes to the broader field of financial analytics by providing a model that not only predicts stock values with greater accuracy but also adapts to market changes in real-time. This adaptability is particularly crucial in an era marked by rapid economic shifts and global interconnectivity levels. The model's versatility and efficacy make it a valuable tool for analysts, traders, and decision-makers, offering them a more reliable means to navigate the complexities of the stock markets. Methodology To enhance efficiency of stock value analysis the proposed DQVPSVP model, represents critical stages, each contributing uniquely to the model's proficiency in predicting stock value patterns. As per Fig. 1 , the 'Data Collection' block serves as the foundation, meticulously gathering extensive financial datasets from the Indian and US stock markets. This block is not just a repository of historical prices but a dynamic amalgamation of diverse financial indicators, encompassing daily stock prices, trading volumes, and other pivotal market data samples. Transitioning from data acquisition to analysis, the 'VARMAx' block emerges as a cornerstone of the model's econometric strength for different scenarios. Here, the Vector Autoregressive Moving Average model with eXogenous inputs intricately weaves together both internal dynamics of stock prices and external factors, such as global indices and samples. This block's main utility is to capture the complex relationships between various market entities and integrate them into a cohesive predictive framework for predictive analysis. The 'Deep Dyna Q Network (DDQN)' block represents the model's adaptive intelligence. DDQN, a sophisticated reinforcement learning algorithm, dynamically tunes the hyperparameters of the VARMAx model process. This block is used to enhance model's adaptive capability by constantly learning and evolving based on feedback from the market's ever-changing landscapes. The fusion of VARMAx framework and the DDQN algorithm represents a sophisticated fusion of econometric theory and advanced machine learning operations. The detail architecture is explained below. Figure 2 illustrates the model architecture for the proposed stock analysis method. The experimental setup for this work is meticulously designed to evaluate the model's effectiveness in predicting real-time changes in stock value patterns, particularly in the Indian and US stock markets. Dataset Details The study employs two distinct datasets, one representing the Indian stock market and the other representing the US stock market. These datasets encompass a comprehensive range of stock data, including opening and closing prices, highs and lows, trading volumes, and other relevant financial indicators for different scenarios. Indian Stock Market Dataset : This dataset includes daily stock prices from the National Stock Exchange (NSE) of India, covering a period of five years (2018–2023). It comprises data from 500 listed companies, representing various sectors such as technology, healthcare, and finance. US Stock Market Dataset : The dataset for the US market is sourced from the New York Stock Exchange (NYSE), including daily stock prices of 500 companies across diverse sectors for the same five-year period (2018–2023). Experimental Parameters and Setup The DQVPSVP model is fine-tuned with a set of parameters to optimize its performance in predicting stock values. The key parameters include Learning Rate: Initially set at 0.01, adjusted dynamically by the Deep Dyna Q algorithm. Epochs: Each training session comprises 100 epochs. Batch Size: Set at 32, allowing for a balanced approach between computational efficiency and training stability. VARMAx Model Settings: Order of autoregression (p) set to 5, moving average components (q) set to 5, and the number of exogenous inputs (x) varies based on the number of external factors considered (e.g., global indices, commodity prices). Deep Dyna Q Settings: Exploration rate initially set at 0.5, with a decay factor of 0.01. The experimental setup involves training the model separately on each dataset. The performance metrics – precision, accuracy, recall, delay, AUC, and specificity – are computed for various test stock sample sizes ranging from 12,000 to 150,000, providing insights into the model's scalability and robustness. Data Preprocessing Prior to model training, the datasets undergo several preprocessing steps Normalization : Stock price data are normalized using the Min-Max scaling technique to enhance model training efficiency. Feature Engineering : Technical indicators such as Moving Averages, Relative Strength Index (RSI), and Bollinger Bands are computed and included as input features. Data Partitioning : The datasets are divided into training (70%), validation (15%), and testing (15%) sets. Evaluation Methodology The model's performance is evaluated using a cross-validation approach, ensuring the robustness of the results. Performance metrics are calculated for each fold, and the average values are reported. In summary, the experimental setup for the DQVPSVP model is comprehensively designed to assess its efficacy in predicting stock value patterns in real-time. The utilization of extensive datasets from the Indian and US stock markets, combined with meticulous parameter tuning and rigorous evaluation methods, ensures a thorough examination of the model's capabilities and potential applications in the domain of financial analytics. Based on this strategy, the Precision (P), Accuracy (A), Recall (R), and Specificity (Sp) levels were estimated via equations 10, 11, 12 & 13 as follows, \(\:Precision\:=\frac{TP}{TP\:+\:FP}\) …(10) \(\:Accuracy\:=\frac{TP\:+\:TN}{TP\:+\:TN\:+\:FP\:+\:FN}\) …(11) \(\:Recall\:=\frac{TP}{TP\:+\:FN}\) …(12) \(\:Specificity\:=\frac{TN}{TN\:+\:FP}\) …(13) The architecture depicted in Fig. 2 is described as follows. Initially, the model begins with the collection of stock samples S= {s1​, s2​,..., sn​}, where each sample encapsulates essential market data samples. The VARMAx component of the model, fundamentally an extension of the Vector Autoregressive (VAR) model, is defined via Eq. 1, \(\:Yt=\mu\:+\sum\:_{i=1}^{p}\varPhi\:iY(t-i)+\sum\:_{j=1}^{q}\varTheta\:j\epsilon\:(t-j)+Xt\beta\:+\epsilon\:t\) …(1) Where, Yt ​ represents the vector of endogenous variables (stock prices & volumes of stocks) at time t , µ is a constant term, Φ i ​ are the coefficients of the autoregressive (AR) terms, Θ j ​ are the coefficients of the moving average (MA) terms, Xt ​ represents exogenous variables (global indices), β is the coefficient matrix for the exogenous inputs, and εt ​ represents the error terms. The model further incorporates technical indicators as primary parameters. For instance, the Simple Moving Average (SMA) is calculated via Eq. 2, \(\:SMAt=\frac{1}{m}\sum\:_{i=0}^{m-1}P(t-i)\) …(2) Where, Pt ​ represents the stock price at time t and m is the period of the SMA process. The Relative Strength Index (RSI), another crucial technical indicator, is via Eq. 3, \(\:RSIt=100-\frac{100}{1+RSt}\) …(3) Where, RSt ​ is the ratio of average gains to average losses over an augmented set of specified timestamp instance levels. The model then integrates these indicators into the VARMAx process, enhancing its predictive capabilities. The error correction model, a key component of VARMAx, is then represented via Eq. 4, \(\:\varDelta\:Yt=\alpha\:\left(Y\left(t-1\right)-{Y}^{{\prime\:}}\left(t-1\right)\right)+\sum\:_{i=1}^{p-1}\varPhi\:\left({i}^{{\prime\:}}\right)\varDelta\:Y\left(t-i\right)+\epsilon\:{t}^{{\prime\:}}\) …(4) Where, Δ Yt ​ is the difference operator, α is the error correction term, and Φ i ′​ are the coefficients of the difference terms. Transitioning to the DDQN, the model employs a state-action-reward-state-action (SARSA) learning process. The state value function under policy π is given via Eq. 5, \(\:V\pi\:\left(s\right)=E\left[Rt+\gamma\:V\pi\:\left(St+1\right)∣St=s\right]\) …(5) Where, Rt ​ is the reward at time t , γ is the discount factor, and S(t + 1​) represents the subsequent states. The action value function, or Q Function, is expressed via Eq. 6, \(\:Q\pi\:\left(s,a\right)=E\left[\begin{array}{c}Rt+\\\:\gamma\:Q\pi\:\left(St+1,At+1\right)\end{array}∣\begin{array}{c}St=s,\\\:At=a\end{array}\right]\) …(6) The DDQN updates the Q values based on the temporal-difference (TD) error, defined via Eq. 7, \(\:\delta\:t=Rt+\gamma\:Q\left(St+1,At+1;\theta\:-\right)-Q\left(St,At;\theta\:\right)\) …(7) Where, θ and θ − are the parameters of the primary and target networks in DDQN, respectively for different stock value samples. The model dynamically tunes the hyperparameters of VARMAx using a policy gradient approach, where the policy π ( a ∣ s ; θ ) is updated via Eq. 8, \(\:\theta\:\left(t+1\right)=\theta\:\left(t\right)+\alpha\:*\delta\:t*\nabla\:\theta\:log\pi\:\left(At∣St;\theta\:t\right)\) …(8) Where, α is the learning rate for this process. The loss function used for training the DDQN, is given via Eq. 9, \(\:L\left(\theta\:\right)=E\left[{\left(\delta\:t\right)}^{2}\right]\) …(9) This loss is minimized to optimize the model’s predictive performance levels. The fusion of VARMAx and DDQN concludes in the prediction module, where the final predicted stock value Y ’ is obtained using the optimized parameters for different use cases. The output of the model for each stock sample si ​ is a predicted value y ’​ I ​, thereby completing the process from input data collection to final stock value prediction process. This fusion of VARMAx with DDQN, articulated through a series of complex equations, establishes a robust, dynamic, and highly precise framework for predicting stock value patterns. The methodology underscores the model’s unique capability to adapt to and accurately forecast market dynamics, setting a new benchmark in the realm of financial analytics. The following section of this paper discusses an example use case for this procedure, followed by a detailed performance analysis of the suggested model in comparison to existing techniques. Sample Case Study The intricate process of stock value prediction using the DQVPSVP model involves several critical stages, each contributing distinctively to the model's overall efficacy. This narrative unfolds through three primary phases: Data Collection, VARMAx processing, and the application of Deep Dyna Q Network (DDQN) optimized VARMAx. Initially, the model embarks on the Data Collection phase, where it acquires actual stock values. This stage is crucial as it forms the empirical backbone of the entire predictive process. Consider a set of network requests that retrieves stock samples from a specific market. The Table 1 represents a snippet of such collected data samples. Table 1 Sample Snippet of data samples Stock ID Date Opening Price Highest Price Lowest Price Closing Price Volume JIO 2024-01-01 150.5 155.2 149.8 154.3 1,000,000 JIO 2024-01-02 154.3 156.4 153.1 155.8 1,200,000 JIO 2024-01-03 155.8 157.5 154.6 156.2 1,500,000 This data is foundational, providing the raw inputs from which sophisticated analyses are derived for different use cases. Next, the model transitions to the VARMAx phase, where it applies a sophisticated algorithm to analyze the temporal relationships inherent in the stock data samples. The VARMAx model, utilizing its capacity to handle multiple time series and incorporate exogenous factors, yields an initial set of predictions. The Table 2 illustrates these predictive outputs: Table 2 Predictive outputs Stock ID Date Predicted Closing Price (VARMAx) JIO 2024-01-04 156.9 JIO 2024-01-05 157.3 JIO 2024-01-06 157.8 These predictions, while insightful, are further refined in the subsequent phase. In the final stage, the DDQN Optimized VARMAx, the model leverages the DDQN algorithm's capacity for hyperparameter optimization. This enhances the model's predictive accuracy by dynamically adjusting to the stock's volatility and market trends. The Table 3 showcases the refined predictive outputs post-DDQN optimization: Table 3 Refined Predictive outputs post-DDQN optimization Stock ID Date Predicted Closing Price (DDQN Optimized VARMAx) JIO 2024-01-04 157.1 JIO 2024-01-05 157.6 JIO 2024-01-06 158.2 The progression from initial data collection, through the VARMAx predictive phase, to the DDQN-optimized predictions represents a journey from raw data to refined, actionable insights. Each step in this process adds layers of complexity and precision, ultimately rendering the model not just a predictive tool but a sophisticated analytical apparatus capable of navigating the complexities of financial markets with remarkable acumen for different value sets. 3 Result Analysis and Comparisons In the proposed research, the innovative fusion of the Vector Autoregressive Moving Average with eXogenous inputs (VARMAx) framework and the Deep Dyna Q algorithm represents a ground breaking shift in stock value prediction methodology. At the heart of this approach lies the strategic use of technical indicators as primary parameters, which are adeptly integrated with global indices, serving as exogenous factors in the VARMAx process. This integration forms a robust foundation, adept at capturing the intricate dependencies inherent in stock values and patterns. The VARMAx model, known for its econometric rigor, is thereby enhanced to handle the multifaceted nature of financial markets with heightened accuracy. Complementing this, the Deep Dyna Q algorithm emerges as a critical component in this architecture, dynamically tuning the hyperparameters of the VARMAx model. Its deployment signifies a leap in the adaptability of the prediction model, enabling it to continuously adjust to varying stock types and market conditions. This adaptive mechanism is not just a mere adjustment but a comprehensive recalibration of the model's predictive capabilities, ensuring that the predictions remain precise and relevant across different market scenarios. The empirical validation of this model, conducted through rigorous testing on diverse datasets from the Indian and USA stock markets, further underscores its efficacy and adaptability levels. The model is assessed using evaluation parameters such as Precision (P), Accuracy (A), Recall (R), Delay, AUC and Specificity (Sp). Based on this analysis, the precision achieved during stock value prediction operations is compared with LightGBM [ 3 ], Graph Evolution Recurrent Unit (GERU) [ 4 ], and FinGAT [ 15 ], as highlighted in Fig. 3 . In the analysis of various numbers of test stock samples (NTS), the DQVPSVP model consistently outperforms other models. For example, with 12k NTS, DQVPSVP achieves a precision of 93.79%, compared to LightGBM's [ 3 ] 84.30%, GERU's [ 4 ] 85.63%, and FinGAT's [ 15 ]86.63%. This superiority is maintained with larger sample sizes: at 60k NTS, DQVPSVP's precision is 93.48%, versus LightGBM's 75.52%, GERU's 94.11%, and FinGAT's 81.62%. With 150k NTS, DQVPSVP achieves 94.43%, still outperforming LightGBM (84.55%), GERU (93.28%), and FinGAT (87.19%). This indicates that DQVPSVP's performance remains robust with increasing data volume, crucial for real-time financial analytics with vast and expanding datasets. Similarly, the model is evaluated for accuracy, and the comparative analysis of the models is shown in Fig. 4 below. Figure 4 shows varying accuracy across different numbers of test stock samples (NTS). Notably, some models outperform others in specific instances. For example, with 42k NTS, LightGBM achieves 92.55% accuracy, surpassing DQVPSVP's 90.28%. However, with 78k NTS, DQVPSVP excels with 94.78% accuracy, higher than LightGBM's 87.73%, GERU's 75.81%, and Fin-GAT's 81.05%. This highlights DQVPSVP's strong but context-dependent performance. DQVPSVP's varying accuracy might stem from its sophisticated Deep Dyna Q and VARMAx framework, which adapts dynamically to complex stock market dynamics. This adaptability can cause variability in accuracy, especially in rapidly changing markets. Its real-time hyperparameter tuning adjusts to different stock types and market conditions, impacting accuracy. High prediction accuracy reduces investment errors and increases profitability. The variability among models and NTS sizes underscores the importance of choosing models based on specific market conditions and data volumes. LightGBM might be more reliable in some cases, while DQVPSVP's advanced features may offer an edge in others. Similar to this, Fig. 5 represents the recall levels is as follows. Figure 5 shown above illustrates the recall levels for various models across different numbers of test stock samples (NTS). For example, with 12k NTS, DQVPSVP achieves a recall of 89.13%, significantly higher than LightGBM's 76.60% and nearly matching GERU's 89.04%. This trend continues across most NTS sizes. At 60k NTS, DQVPSVP records a recall of 92.59%, surpassing LightGBM's 89.05% and GERU's 78.53%. In real-time stock trading, a high recall rate, like DQVPSVP's, is crucial for capitalizing on profitable opportunities. It ensures the model captures significant positive stock movements, providing timely insights and reducing the risk of missed opportunities, which is vital in fast-paced trading environments. DQVPSVP's consistent recall performance across various sample sizes indicates its robustness and scalability. This is critical in the financial domain, where data volumes and transaction numbers can be immense. A model that maintains high recall rates across different data volumes ensures comprehensive and accurate market coverage. The delay required for the prediction procedure is visualized in a similar manner in Fig. 6 as follows. Analyzing delay data for various models, including LightGBM, GERU, FinGAT, and DQVPSVP, across different numbers of test stock samples (NTS) reveals significant insights. The DQVPSVP model consistently demonstrates lower delay times compared to the other models. For example, at 12k NTS, DQVPSVP shows a delay of 121.15 ms, significantly lower than LightGBM's 156.78 ms, GERU's 145.84 ms, and FinGAT's 136.96 ms. This pattern persists at 72k NTS, with DQVPSVP recording a delay of 125.04 ms, compared to LightGBM's 161.90 ms, GERU's 162.39 ms, and FinGAT's 150.07 ms. The lower delay in DQVPSVP can be attributed to its efficient integration of the Deep Dyna Q algorithm with the VARMAx framework, enabling faster processing and prediction times. This efficiency is crucial in stock market scenarios, where real-time data processing and quick decision-making are paramount. In high-frequency trading environments, even a small delay can result in missed opportunities or substantial financial losses due to rapid stock price fluctuations. Similarly, the AUC levels can be observed from Fig. 7 as follows. The DQVPSVP model consistently shows high AUC values across various NTS sizes, indicating superior stock movement classification. For instance, at 12k NTS, DQVPSVP achieves an AUC of 85.62%, surpassing LightGBM's 78.78%, GERU's 82.04%, and FinGAT's 76.42%. At 150k NTS, DQVPSVP's AUC reaches 98.22%, significantly outperforming the other models. This high AUC performance is due to DQVPSVP's advanced integration of the Deep Dyna Q algorithm with the VARMAx framework, enabling effective differentiation between true positive and true negative predictions. In real-time financial scenarios, a high AUC value instills confidence in predictive outputs, aiding investors and traders in making informed decisions. DQVPSVP's consistent high AUC across different data sizes demonstrates its robustness and effectiveness in diverse market conditions. In the volatile financial markets, maintaining high predictive accuracy is essential for various use cases. Similarly, the Specificity levels can be observed from Fig. 8 as follows, At 12k NTS, DQVPSVP achieves an 82.19% specificity, outperforming LightGBM's 78.95%, GERU's 75.22%, and FinGAT's 75.41%. This trend continues at 102k NTS, where DQVPSVP reaches 95.66%, surpassing LightGBM's 84.78%, GERU's 83.68%, and FinGAT's 80.62%. DQVPSVP's higher specificity is due to its integration of the Deep Dyna Q algorithm with the VARMAx framework, which improves its ability to identify true negative stock movements and minimize false positives. This high specificity is crucial in financial trading, as it reduces the risk of misinterpreting stock trends, thus aiding traders and investors in making more accurate decisions. 4 Conclusion and Future Work The DQVPSVP model, an innovative amalgamation of the Vector Autoregressive Moving Average with eXogenous inputs (VARMAx) framework and the Deep Dyna Q algorithm, has demonstrated exceptional proficiency in predicting real-time changes in stock value patterns. Empirical tests on Indian and USA markets show significant improvements: 3.5% in precision, 2.9% in accuracy, 3.9% in recall, 4.5% in Area Under Curve (AUC), and 3.4% in specificity as compared to the existing models like LightGBM[ 3 ], GERU[ 4 ], and FinGAT[ 15 ]. Additionally, it reduces response delay by 1.5%, crucial for timely financial decisions. The implications of these results are substantial. For practitioners in the financial sector, the DQVPSVP model offers a more reliable and efficient tool for stock market analysis, paving the way for more informed investment strategies and risk management. Future work could extend the application of the DQVPSVP model to other financial instruments like bonds, commodities, and cryptocurrencies. This expansion would evaluate the model's versatility and applicability across different market dynamics. Integrating the model into real-time trading systems could offer actionable insights and enable automated trading, marking a significant advancement towards AI-driven financial decision-making. Additionally, incorporating more sophisticated technical indicators and exploring alternative data sources, such as social media sentiment and economic indicators, could further enhance the model's predictive capabilities. Declarations We declare that there is no conflict in the manuscript. The authors declare that they have no conflict of interest. Authors' contributions Rachna Sable contributed to the study conception and design, data collection, data analysis, interpretation, and manuscript drafting. Rachna Sable, Sudhanshu Gupta, and Pallavi Parlewar reviewed, validated the results and all authors approved the final manuscript. Funding: There is no Funding received for this work. References Wang S (2023) A stock price prediction method based on BILSTM and improved transformer. IEEE Access 11:104211–104223. https://doi.org/10.1109/access.2023.3296308 Mu G, Gao N, Wang Y, Li D (2023) A stock price prediction model based on investor sentiment and optimized deep learning. IEEE Access 11:51353–51367. https://doi.org/10.1109/access.2023.3278790 Zhao X, Liu Y, Zhao Q (2023) Cost Harmonization LightGBM-Based Stock Market Prediction. IEEE Access 11:105009–105026. https://doi.org/10.1109/access.2023.3318478 Tian H, Zhang X, Zheng X, Zeng D (2023) Learning dynamic dependencies with graph evolution recurrent unit for stock predictions. IEEE Trans Syst Man Cybernetics Syst 53(11):6705–6717. https://doi.org/10.1109/tsmc.2023.3284840 Wang H, Wang T, Li S, Guan S (2022) HATR-I: Hierarchical Adaptive temporal Relational Interaction for stock trend prediction. IEEE Trans Knowl Data Eng 1–14. https://doi.org/10.1109/tkde.2022.3188320 Choi J, Yoo S, Zhou X, Kim Y (2023) Hybrid Information Mixing Module for stock movement prediction. IEEE Access 11:28781–28790. https://doi.org/10.1109/access.2023.3258695 Chiong R, Fan Z, Hu Z, Dhakal S (2023) A novel ensemble learning approach for stock market prediction based on sentiment analysis and the sliding window method. IEEE Trans Comput Social Syst 10(5):2613–2623. https://doi.org/10.1109/tcss.2022.3182375 Sidogi T, Mongwe WT, Mbuvha R, Olukanmi P, Marwala T (2023) A signature transform of limit order book data for stock price prediction. 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IEEE Access 11:10275–10287. https://doi.org/10.1109/access.2023.3240422 Khuwaja P, Khowaja SA, Dev K (2023) Adversarial learning networks for FinTech applications using heterogeneous data sources. IEEE Internet Things J 10(3):2194–2201. https://doi.org/10.1109/jiot.2021.3100742 Hsu YL, Tsai YC, Li C (2022) FINGAT: Financial Graph Attention Networks for recommending Top-K Profitable stocks. IEEE Trans Knowl Data Eng 1. https://doi.org/10.1109/tkde.2021.3079496 Lee N, Moon J (2023) Offline Reinforcement learning for automated stock trading. IEEE Access 11:112577–112589. https://doi.org/10.1109/access.2023.3324458 Singh P, Jha MK, Sharaf M, El-Meligy MA, Gadekallu TR (2023) Harnessing a hybrid CNN-LSTM model for portfolio Performance: A case study on stock selection and optimization. IEEE Access 11:104000–104015. https://doi.org/10.1109/access.2023.3317953 Chen C, Shih P, Srivastava G, Hung S, Lin JC (2023) Evolutionary trading signal prediction model optimization based on Chinese news and technical indicators in the internet of things. IEEE Internet Things J 10(3):2162–2173. https://doi.org/10.1109/jiot.2021.3085714 Ahmed U, Lin JC, Srivastava G, Yun U (2023) Enhancing stock portfolios for enterprise management and investment in energy industry. IEEE Trans Industr Inf 19(6):7667–7675. https://doi.org/10.1109/tii.2022.3214518 Feili H, Li L, Leimingding (2023) A Medium to Long-Term Multi-Influencing Factor Copper Price Prediction Method based on CNN-LSTM. IEEE Access 11:69458–69473. https://doi.org/10.1109/access.2023.3288486 Zhou Z, Song Z, Ren T, Yu L (2023) Two-Stage portfolio optimization integrating optimal sharp ratio measure and ensemble learning. IEEE Access 11:1654–1670. https://doi.org/10.1109/access.2022.3232281 Li B, Luo J, Xu H (2023) A portfolio selection strategy based on the peak price involving randomness. IEEE Access 1. https://doi.org/10.1109/access.2023.3278980 Khattak BHA, Shafi I, Khan AS, Flores ES, Lara RG, Samad MA, Ashraf I (2023) A Systematic survey of AI models in Financial Market Forecasting for Profitability analysis. IEEE Access 11:125359–125380. https://doi.org/10.1109/access.2023.3330156 Mi J, Liu L, Zhuang Y, Bai L, Li Y (2023) A synthetic feature processing method for remaining useful life prediction of rolling bearings. IEEE Trans Reliab 72(1):125–136. https://doi.org/10.1109/tr.2022.3192526 Zhang M, Ding D, Pan X, Yang M (2021) Enhancing Time Series Predictors with Generalized Extreme Value Loss. IEEE Trans Knowl Data Eng 1. https://doi.org/10.1109/tkde.2021.310 Han C, Fu X (2023) Challenge and opportunity: deep learning-based stock price prediction by using Bi-directional LSTM model. Front Bus Econ Manage 8(2):51–54 Mehtab S, Sen J, Dutta A (2021) Stock price prediction using machine learning and LSTM-based deep learning models. In Machine Learning and Metaheuristics Algorithms, and Applications: Second Symposium, SoMMA 2020, Chennai, India, October 14–17, 2020, (pp. 88–106). Springer Singapore Abe M, Nakayama H (2018) Deep learning for forecasting stock returns in the cross-section. In Advances in Knowledge Discovery and Data Mining: 22nd Pacific-Asia Conference, PAKDD 2018, Melbourne, VIC, Australia, June 3–6, 2018, Proceedings, Part I 22 (pp. 273–284). Springer International Publishing Kamalov F, Gurrib I, Rajab K (2021) Financial forecasting with machine learning: price vs return. J Comput Sci 17(3):251–264 Additional Declarations No competing interests reported. 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Sable","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA6klEQVRIiWNgGAWjYHACNgglwdzA8AHEZSdeC2MD4wwQl5kULcw8IAYhLebth589LqhhsOef3dj42ObXNnk+ZgbGDx9zcGuROZNmbjzjGEPijDsHm41z+24btjEzMEvO3IZbiwRDDps0DxtDAsONxDbp3J7bjEAtbMy8+LTwvwFq+cdgL38jsf23Zc9te8JaJIC28LYxMG4A2sLM8ON2IhFanplJ8/ZJJG4E+kWyt+F2chszYzN+v/AnP5Pm+WZjL3e7+eCHH39u285vBzI+4tECDwUwYGwDkw0E1SOBP6QoHgWjYBSMgpECAMXkSdHl+RdUAAAAAElFTkSuQmCC","orcid":"","institution":"Bennett University","correspondingAuthor":true,"prefix":"","firstName":"Rachna","middleName":"","lastName":"Sable","suffix":""},{"id":399982601,"identity":"8dcf40dd-4ebc-45c8-8c5c-aa6c87a43454","order_by":1,"name":"Aman Singh","email":"","orcid":"","institution":"MIT-ADT University","correspondingAuthor":false,"prefix":"","firstName":"Aman","middleName":"","lastName":"Singh","suffix":""},{"id":399982602,"identity":"908df5d7-0e7d-41ca-8d25-d34c33d6ad9b","order_by":2,"name":"Sudhanshu 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1","display":"","copyAsset":false,"role":"figure","size":116304,"visible":true,"origin":"","legend":"\u003cp\u003eOverall Flow of the Proposed Model used for Stock Value Analysis\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-5794220/v1/21ce3f2f4f665eaeee35afc6.png"},{"id":73652967,"identity":"f466120c-c5e5-4c49-8945-0fbebe7bcae8","added_by":"auto","created_at":"2025-01-13 09:54:21","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":147598,"visible":true,"origin":"","legend":"\u003cp\u003eModel Architecture for the Proposed Method for Stock Analysis\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-5794220/v1/3144a767c1d65457dab784f8.png"},{"id":73652963,"identity":"ef32f2a2-cc0c-4f39-9692-4c4781d9e9d7","added_by":"auto","created_at":"2025-01-13 09:54:20","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":41444,"visible":true,"origin":"","legend":"\u003cp\u003ePrecision observed for prediction of stock value sets\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-5794220/v1/815574b287dc9a7e437bcc93.png"},{"id":73653041,"identity":"37c79a73-46e6-4f48-a31f-d54974a14209","added_by":"auto","created_at":"2025-01-13 09:54:24","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":69677,"visible":true,"origin":"","legend":"\u003cp\u003eAccuracy observed for prediction of stock value sets\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-5794220/v1/345ea225312c58c59291a9cf.png"},{"id":73652930,"identity":"f65a5f2a-7aee-4bf6-9b98-0c5032478d0f","added_by":"auto","created_at":"2025-01-13 09:54:19","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":65674,"visible":true,"origin":"","legend":"\u003cp\u003eRecall observed for prediction of stock value sets\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-5794220/v1/b811cd1b6225244ba4a54c92.png"},{"id":73653138,"identity":"93b7bd1d-175b-4b0c-affd-0dc91a9a1b50","added_by":"auto","created_at":"2025-01-13 09:54:25","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":116914,"visible":true,"origin":"","legend":"\u003cp\u003eDelay needed for prediction of stock value sets\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-5794220/v1/f79f59774eb988a53d7a9622.png"},{"id":73653195,"identity":"49156d23-e48b-4006-8c98-93c19d0ed8b0","added_by":"auto","created_at":"2025-01-13 09:54:35","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":111092,"visible":true,"origin":"","legend":"\u003cp\u003eAUC observed for prediction of stock value sets\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-5794220/v1/bb80e431d879c57ddb516cda.png"},{"id":73653198,"identity":"30c0f1d4-3850-4979-99e3-6390dc316c54","added_by":"auto","created_at":"2025-01-13 09:54:35","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":109159,"visible":true,"origin":"","legend":"\u003cp\u003eSpecificity observed for prediction of stock value sets\u003c/p\u003e","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-5794220/v1/53122f4e423a58e6c0c6644b.png"},{"id":73974367,"identity":"ffc66c5e-4550-41f3-b391-4de5ab409f3e","added_by":"auto","created_at":"2025-01-16 14:09:24","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1467488,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5794220/v1/0726db7f-b83c-4024-a0ae-a29814699a4e.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Designing an efficient Deep Dyna Q based VARMAx Model for Prediction of Real-Time changes in Stock Value Patterns","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eThe introduction of computational techniques in finance has marked a significant shift from traditional methods, offering a more nuanced understanding of market dynamics. However, despite the advancements, existing models often struggle to keep pace with the rapidly evolving and complex nature of stock markets. This gap underscores a critical need for more sophisticated, adaptive models that can effectively interpret and predict real-time changes in stock values.\u003c/p\u003e \u003cp\u003eThe introduction of Vector Autoregressive Moving Average with eXogenous inputs (VARMAx) models marked significant progress by incorporating external factors and historical data to capture complex interactions in financial markets. However, their static hyperparameters pose a limitation, as they cannot adapt to changing market conditions, leading to potentially suboptimal predictions. To address this, the current work integrates the robust forecasting capabilities of VARMAx with the adaptive power of Deep Dyna Q algorithms. This integration enhances stock value predictions' responsiveness and accuracy by using Deep Dyna Q, a reinforcement learning algorithm, to continuously adjust VARMAx hyperparameters in real-time, accommodating various stock types and market conditions.\u003c/p\u003e \u003cp\u003eIn conclusion, this introduction sets the stage for a detailed exploration of the proposed model, its methodological framework, the rationale behind its design, and its impactful contributions to the field of financial analytics. The subsequent sections will delve deeper into the technical aspects of the model, the nuances of its implementation, and a comprehensive analysis of its performance, thereby unfolding the full narrative of this innovative approach to stock value predictions.\u003c/p\u003e"},{"header":"2 Literature review","content":"\u003cp\u003eAs shown through various research studies, the recent advancements in stock price prediction methodologies underscore the significant strides made in financial technology. This literature review synthesizes insights from fifteen notable studies, each contributing uniquely to the understanding of stock market dynamics and predictive analytics.\u003c/p\u003e \u003cp\u003eAn innovative method for stock price prediction using a combination of BiLSTM and an improved transformer model was developed by [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. This approach highlighted the efficacy of integrating deep learning techniques for financial forecasting. Similarly, work by [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e] emphasized the role of investor sentiment in stock price prediction, utilizing optimized deep learning methods to enhance prediction accuracy. These studies collectively underscore the growing reliance on complex algorithms in financial market analysis. The work by [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e] introduced a Cost Harmonization LightGBM-based model for stock market prediction, highlighting a novel approach in utilizing gradient boosting frameworks. The work by [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e] advanced this discussion by illustrating the use of Graph Evolution Recurrent Unit for learning dynamic dependencies in stock predictions, emphasizing the importance of understanding temporal relationships in financial data samples. [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e] investigated hierarchical adaptive temporal relational interaction using their HATR-I model to forecast stock trends, emphasising the importance of relational and temporal dynamics in market analysis. [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] proposed a Hybrid Information Mixing Module for stock movement prediction, thereby stressing the integration of diverse data sources for improved accuracy. [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e] proposed a unique ensemble learning strategy for stock market prediction that combines sentiment analysis and the sliding window method. This study demonstrated the increased importance on sentiment analysis in financial forecasting. [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e] focused on the Signature Transform of Limit Order Book Data for stock price prediction, highlighting the potential of order book data in predictive analysis.\u003c/p\u003e \u003cp\u003e[\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e] discussed the Transformer-Gated Recurrent Unit Method for predicting stock prices based on news sentiments and technical indicators. This approach emphasized the multifaceted nature of stock market prediction, where various external and internal factors were considered. [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e] provided a comprehensive view of artificial intelligence applications in the economy, including stock trading and market analysis, underlining the broader context of AI in financial decision-making.[\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e] explored the realm of reinforcement learning for stock prediction, specifically addressing high-frequency trading with T\u0026thinsp;+\u0026thinsp;1 rules. This study exemplifies the application of reinforcement learning in a practical trading context. [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e] focused on the exploitation of macroeconomic indicators for stock direction classification, using the Multimodal Fusion Transformer to integrate diverse economic indicators into predictive models.[\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e] delve into adversarial learning networks for FinTech applications using heterogeneous data sources, suggesting the potential of adversarial networks in handling diverse financial data samples. [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e] introduced FinGAT, a financial graph attention network for recommending profitable stocks, highlighting the use of attention mechanisms in stock selection. [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e] explored the application of offline reinforcement learning in automated stock trading. This study represented a critical step forward in the application of reinforcement learning techniques, particularly in the context of environments where real-time interaction is not feasible. [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e] presented a hybrid CNN-LSTM model for portfolio performance, focusing on stock selection and optimization. This model exemplifies the effective combination of convolutional and recurrent neural networks in financial applications, offering insights into the utility of deep learning architectures in stock market analytics.\u003c/p\u003e \u003cp\u003e[\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e] delve into an evolutionary trading signal prediction model, optimized based on Chinese news and technical indicators within the Internet of Things framework. This study underscores the significance of integrating diverse data sources, including news sentiment, for enhancing predictive accuracy in trading models. [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e] contributed to the field by enhancing stock portfolios for enterprise management and investment, specifically in the energy industry. Their work illustrated the sector-specific application of stock market predictions, emphasizing the contextual adaptation of predictive models. [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e] proposed a medium to long-term multi-influencing factor copper price prediction method utilizing a CNN-LSTM network. This approach is notable for its application to commodity price prediction, extending the scope of predictive analytics beyond traditional stock prices. [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e] introduced a two-stage portfolio optimization integrating an optimal sharp ratio measure and ensemble learning. This study is pivotal in illustrating the application of ensemble methods in optimizing financial portfolios, emphasizing the balance between risk and return. [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e] discussed a portfolio selection strategy based on peak price involving randomness. This approach adds to the understanding of stochastic elements in financial decision-making. [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e] provided a systematic survey of AI models in financial market forecasting for profitability analysis. Their comprehensive review offered a broad perspective on the various methodologies and their effectiveness in financial forecasting. [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e] discussed a synthetic feature processing method for remaining useful life prediction of rolling bearings. While distinct from stock market prediction, this study highlights the broader applicability of predictive models in different domains of reliability engineering. Finally, [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e] enhanced time series predictors with a generalized extreme value loss. This advancement in loss function optimization has implications for improving the accuracy and robustness of predictive models in time series analysis. [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e] proposed a bi-directional long short-term memory (Bi-LSTM) model for predicting future stock prices based on historical data. Unlike standard LSTM, Bi-LSTM captures both short- and long-term dependencies by processing sequences forward and backward. Applied to Apple's stock price data, the model's performance was evaluated using mean squared error (MSE) and visual comparison of actual vs. predicted prices. The experiments showed Bi-LSTM makes accurate predictions and captures trends, though it may struggle with sudden market changes. Overall, it was concluded that Bi-LSTM is a promising tool for stock price prediction with many potential applications in finance. A hybrid modeling approach for stock price prediction, combining machine learning and deep learning models was proposed by [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. Using NIFTY 50 index dataset a regression model was used to predict open values. The framework was then enhanced with four deep learning-based regression models using LSTM networks and walk-forward validation. Optimized through grid-searching, the LSTM models ensured stable validation losses and accuracy convergence. Results showed that LSTM univariate model, using one-week prior data for next week's prediction, is the most accurate. The work in [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e] used deep learning to predict one-month-ahead stock returns in the Japanese market and evaluates its performance. Results showed that deep neural networks outperform shallow networks and other machine learning models, indicating deep learning's potential for predicting stock returns. The effectiveness of stock price and return as input features in directional forecasting models using 10-year historical data from ten large-cap US companies were compared by [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. Employing four popular classification algorithms, the analysis showed that stock price is a more effective standalone input than return. However, their effectiveness equalizes when technical indicators are included. It was concluded that stock price generally outperforms return in predicting price direction, offering valuable insights for researchers and practitioners in stock price forecasting.\u003c/p\u003e \u003cp\u003eThese studies collectively demonstrate a trend towards more sophisticated, data-driven approaches in stock trading and portfolio management. They emphasize the role of machine learning, particularly deep learning, reinforcement learning, and ensemble methods, in decoding complex market dynamics. The integration of diverse data sources, including news sentiment and technical indicators, further enriches the predictive capabilities of these models. This body of work advances financial technology and provides valuable insights for practitioners and researchers in developing more effective and efficient predictive models for financial markets.\u003c/p\u003e \u003cp\u003eIn summary, the literature in ML-based stock market analysis reflects a trajectory of increasing sophistication and complexity, moving from simple linear models to advanced neural networks and adaptive learning algorithms. Each stage in this evolution has contributed to a deeper understanding and more accurate prediction of stock market behavior, culminating in the current trend of integrating diverse data sources and employing adaptive algorithms for real-time analysis.\u003c/p\u003e \u003cp\u003e \u003cb\u003eMotivation \u0026amp; Contributions\u003c/b\u003e \u003c/p\u003e \u003cp\u003eThe literature indicates that traditional forecasting models, though foundational, often fail to capture the complex and dynamic nature of the stock market. This limitation is especially pronounced during periods of market volatility, where rapid changes require a predictive model that is both accurate and adaptable in real-time. The inability of these models to adjust to varying market conditions highlights the need for a more advanced approach that can intelligently evolve with the ever-changing financial landscape.\u003c/p\u003e \u003cp\u003eIt is in this context that the current study introduces an innovative model, merging the strengths of VARMAx with the adaptive capabilities of Deep Dyna Q algorithms. The VARMAx model's ability to incorporate external factors and historical data presents a solid foundation for understanding market dynamics. However, the static nature of its hyperparameters limits its adaptability. This limitation forms the crux of our motivation: to enhance the VARMAx model with a mechanism that allows for dynamic adjustment and real-time responsiveness. The integration of Deep Dyna Q algorithms addresses this gap. Renowned for their efficacy in environments requiring continuous learning, these algorithms offer a means to dynamically tune hyperparameters, thereby enabling the model to adjust its predictive strategy in response to market fluctuations. This novel approach not only enhances the accuracy of stock value predictions but also significantly reduces the response time, a critical factor in financial markets where opportunities are fleeting.\u003c/p\u003e \u003cp\u003eThe contributions of this research are multifaceted and substantial. Firstly, it presents a pioneering model that seamlessly blends advanced machine learning techniques with traditional econometric methods, setting a new benchmark in stock market prediction. Secondly, the empirical validation of the model across diverse stock markets, including those of India and the USA, demonstrates its robustness and applicability in varying market conditions. This is evidenced by the model's superior performance metrics, including improved precision, accuracy, recall, AUC, specificity, and reduced delay, compared to existing methods.\u003c/p\u003e \u003cp\u003eMoreover, this research contributes to the broader field of financial analytics by providing a model that not only predicts stock values with greater accuracy but also adapts to market changes in real-time. This adaptability is particularly crucial in an era marked by rapid economic shifts and global interconnectivity levels. The model's versatility and efficacy make it a valuable tool for analysts, traders, and decision-makers, offering them a more reliable means to navigate the complexities of the stock markets.\u003c/p\u003e \u003cp\u003e \u003cb\u003eMethodology\u003c/b\u003e \u003c/p\u003e \u003cp\u003eTo enhance efficiency of stock value analysis the proposed DQVPSVP model, represents critical stages, each contributing uniquely to the model's proficiency in predicting stock value patterns. As per Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, the 'Data Collection' block serves as the foundation, meticulously gathering extensive financial datasets from the Indian and US stock markets.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThis block is not just a repository of historical prices but a dynamic amalgamation of diverse financial indicators, encompassing daily stock prices, trading volumes, and other pivotal market data samples. Transitioning from data acquisition to analysis, the 'VARMAx' block emerges as a cornerstone of the model's econometric strength for different scenarios. Here, the Vector Autoregressive Moving Average model with eXogenous inputs intricately weaves together both internal dynamics of stock prices and external factors, such as global indices and samples. This block's main utility is to capture the complex relationships between various market entities and integrate them into a cohesive predictive framework for predictive analysis.\u003c/p\u003e \u003cp\u003eThe 'Deep Dyna Q Network (DDQN)' block represents the model's adaptive intelligence. DDQN, a sophisticated reinforcement learning algorithm, dynamically tunes the hyperparameters of the VARMAx model process. This block is used to enhance model's adaptive capability by constantly learning and evolving based on feedback from the market's ever-changing landscapes. The fusion of VARMAx framework and the DDQN algorithm represents a sophisticated fusion of econometric theory and advanced machine learning operations. The detail architecture is explained below.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e illustrates the model architecture for the proposed stock analysis method. The experimental setup for this work is meticulously designed to evaluate the model's effectiveness in predicting real-time changes in stock value patterns, particularly in the Indian and US stock markets.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eDataset Details\u003c/strong\u003e \u003cp\u003eThe study employs two distinct datasets, one representing the Indian stock market and the other representing the US stock market. These datasets encompass a comprehensive range of stock data, including opening and closing prices, highs and lows, trading volumes, and other relevant financial indicators for different scenarios.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eIndian Stock Market Dataset\u003c/b\u003e: This dataset includes daily stock prices from the National Stock Exchange (NSE) of India, covering a period of five years (2018\u0026ndash;2023). It comprises data from 500 listed companies, representing various sectors such as technology, healthcare, and finance.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eUS Stock Market Dataset\u003c/b\u003e: The dataset for the US market is sourced from the New York Stock Exchange (NYSE), including daily stock prices of 500 companies across diverse sectors for the same five-year period (2018\u0026ndash;2023).\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eExperimental Parameters and Setup\u003c/strong\u003e \u003cp\u003eThe DQVPSVP model is fine-tuned with a set of parameters to optimize its performance in predicting stock values. The key parameters include\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eLearning Rate: Initially set at 0.01, adjusted dynamically by the Deep Dyna Q algorithm.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eEpochs: Each training session comprises 100 epochs.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eBatch Size: Set at 32, allowing for a balanced approach between computational efficiency and training stability.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eVARMAx Model Settings: Order of autoregression (p) set to 5, moving average components (q) set to 5, and the number of exogenous inputs (x) varies based on the number of external factors considered (e.g., global indices, commodity prices).\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eDeep Dyna Q Settings: Exploration rate initially set at 0.5, with a decay factor of 0.01.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eThe experimental setup involves training the model separately on each dataset. The performance metrics \u0026ndash; precision, accuracy, recall, delay, AUC, and specificity \u0026ndash; are computed for various test stock sample sizes ranging from 12,000 to 150,000, providing insights into the model's scalability and robustness.\u003c/p\u003e \u003cp\u003e \u003cstrong\u003eData Preprocessing\u003c/strong\u003e \u003cp\u003ePrior to model training, the datasets undergo several preprocessing steps\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eNormalization\u003c/b\u003e: Stock price data are normalized using the Min-Max scaling technique to enhance model training efficiency.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eFeature Engineering\u003c/b\u003e: Technical indicators such as Moving Averages, Relative Strength Index (RSI), and Bollinger Bands are computed and included as input features.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eData Partitioning\u003c/b\u003e: The datasets are divided into training (70%), validation (15%), and testing (15%) sets.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eEvaluation Methodology\u003c/strong\u003e \u003cp\u003eThe model's performance is evaluated using a cross-validation approach, ensuring the robustness of the results. Performance metrics are calculated for each fold, and the average values are reported.\u003c/p\u003e \u003c/p\u003e \u003cp\u003eIn summary, the experimental setup for the DQVPSVP model is comprehensively designed to assess its efficacy in predicting stock value patterns in real-time. The utilization of extensive datasets from the Indian and US stock markets, combined with meticulous parameter tuning and rigorous evaluation methods, ensures a thorough examination of the model's capabilities and potential applications in the domain of financial analytics. Based on this strategy, the Precision (P), Accuracy (A), Recall (R), and Specificity (Sp) levels were estimated via equations 10, 11, 12 \u0026amp; 13 as follows,\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Taba\" border=\"1\"\u003e \u003ccolgroup cols=\"2\"\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 \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:Precision\\:=\\frac{TP}{TP\\:+\\:FP}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026hellip;(10)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:Accuracy\\:=\\frac{TP\\:+\\:TN}{TP\\:+\\:TN\\:+\\:FP\\:+\\:FN}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026hellip;(11)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:Recall\\:=\\frac{TP}{TP\\:+\\:FN}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026hellip;(12)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:Specificity\\:=\\frac{TN}{TN\\:+\\:FP}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026hellip;(13)\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\u003eThe architecture depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e is described as follows.\u003c/p\u003e \u003cp\u003eInitially, the model begins with the collection of stock samples S= {s1​, s2​,..., sn​}, where each sample encapsulates essential market data samples. The VARMAx component of the model, fundamentally an extension of the Vector Autoregressive (VAR) model, is defined via Eq.\u0026nbsp;1,\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabb\" border=\"1\"\u003e \u003ccolgroup cols=\"2\"\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 \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:Yt=\\mu\\:+\\sum\\:_{i=1}^{p}\\varPhi\\:iY(t-i)+\\sum\\:_{j=1}^{q}\\varTheta\\:j\\epsilon\\:(t-j)+Xt\\beta\\:+\\epsilon\\:t\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026hellip;(1)\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\u003eWhere, \u003cem\u003eYt\u003c/em\u003e​ represents the vector of endogenous variables (stock prices \u0026amp; volumes of stocks) at time \u003cem\u003et\u003c/em\u003e, \u003cem\u003e\u0026micro;\u003c/em\u003e is a constant term, Φ\u003cem\u003ei\u003c/em\u003e​ are the coefficients of the autoregressive (AR) terms, Θ\u003cem\u003ej\u003c/em\u003e​ are the coefficients of the moving average (MA) terms, \u003cem\u003eXt\u003c/em\u003e​ represents exogenous variables (global indices), \u003cem\u003eβ\u003c/em\u003e is the coefficient matrix for the exogenous inputs, and \u003cem\u003eεt\u003c/em\u003e​ represents the error terms. The model further incorporates technical indicators as primary parameters. For instance, the Simple Moving Average (SMA) is calculated via Eq.\u0026nbsp;2,\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabc\" border=\"1\"\u003e \u003ccolgroup cols=\"2\"\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 \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:SMAt=\\frac{1}{m}\\sum\\:_{i=0}^{m-1}P(t-i)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026hellip;(2)\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\u003eWhere, \u003cem\u003ePt\u003c/em\u003e​ represents the stock price at time \u003cem\u003et\u003c/em\u003e and \u003cem\u003em\u003c/em\u003e is the period of the SMA process. The Relative Strength Index (RSI), another crucial technical indicator, is via Eq.\u0026nbsp;3,\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabd\" border=\"1\"\u003e \u003ccolgroup cols=\"2\"\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 \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:RSIt=100-\\frac{100}{1+RSt}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026hellip;(3)\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\u003eWhere, \u003cem\u003eRSt\u003c/em\u003e​ is the ratio of average gains to average losses over an augmented set of specified timestamp instance levels. The model then integrates these indicators into the VARMAx process, enhancing its predictive capabilities.\u003c/p\u003e \u003cp\u003eThe error correction model, a key component of VARMAx, is then represented via Eq.\u0026nbsp;4,\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabe\" border=\"1\"\u003e \u003ccolgroup cols=\"2\"\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 \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varDelta\\:Yt=\\alpha\\:\\left(Y\\left(t-1\\right)-{Y}^{{\\prime\\:}}\\left(t-1\\right)\\right)+\\sum\\:_{i=1}^{p-1}\\varPhi\\:\\left({i}^{{\\prime\\:}}\\right)\\varDelta\\:Y\\left(t-i\\right)+\\epsilon\\:{t}^{{\\prime\\:}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026hellip;(4)\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\u003eWhere, Δ\u003cem\u003eYt\u003c/em\u003e​ is the difference operator, \u003cem\u003eα\u003c/em\u003e is the error correction term, and Φ\u003cem\u003ei\u003c/em\u003e\u0026prime;​ are the coefficients of the difference terms. Transitioning to the DDQN, the model employs a state-action-reward-state-action (SARSA) learning process.\u003c/p\u003e \u003cp\u003eThe state value function under policy \u003cem\u003eπ\u003c/em\u003e is given via Eq.\u0026nbsp;5,\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabf\" border=\"1\"\u003e \u003ccolgroup cols=\"2\"\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 \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:V\\pi\\:\\left(s\\right)=E\\left[Rt+\\gamma\\:V\\pi\\:\\left(St+1\\right)∣St=s\\right]\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026hellip;(5)\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\u003eWhere, \u003cem\u003eRt\u003c/em\u003e​ is the reward at time \u003cem\u003et\u003c/em\u003e, \u003cem\u003eγ\u003c/em\u003e is the discount factor, and \u003cem\u003eS(t\u003c/em\u003e\u0026thinsp;+\u0026thinsp;1​) represents the subsequent states. The action value function, or Q Function, is expressed via Eq.\u0026nbsp;6,\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabg\" border=\"1\"\u003e \u003ccolgroup cols=\"2\"\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 \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:Q\\pi\\:\\left(s,a\\right)=E\\left[\\begin{array}{c}Rt+\\\\\\:\\gamma\\:Q\\pi\\:\\left(St+1,At+1\\right)\\end{array}∣\\begin{array}{c}St=s,\\\\\\:At=a\\end{array}\\right]\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026hellip;(6)\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\u003eThe DDQN updates the Q values based on the temporal-difference (TD) error, defined via Eq.\u0026nbsp;7,\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabh\" border=\"1\"\u003e \u003ccolgroup cols=\"2\"\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 \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\delta\\:t=Rt+\\gamma\\:Q\\left(St+1,At+1;\\theta\\:-\\right)-Q\\left(St,At;\\theta\\:\\right)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026hellip;(7)\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\u003eWhere, \u003cem\u003eθ\u003c/em\u003e and \u003cem\u003eθ\u003c/em\u003e\u0026thinsp;\u0026minus;\u0026thinsp;are the parameters of the primary and target networks in DDQN, respectively for different stock value samples. The model dynamically tunes the hyperparameters of VARMAx using a policy gradient approach, where the policy \u003cem\u003eπ\u003c/em\u003e(\u003cem\u003ea\u003c/em\u003e∣\u003cem\u003es\u003c/em\u003e;\u003cem\u003eθ\u003c/em\u003e) is updated via Eq.\u0026nbsp;8,\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabi\" border=\"1\"\u003e \u003ccolgroup cols=\"2\"\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 \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\theta\\:\\left(t+1\\right)=\\theta\\:\\left(t\\right)+\\alpha\\:*\\delta\\:t*\\nabla\\:\\theta\\:log\\pi\\:\\left(At∣St;\\theta\\:t\\right)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026hellip;(8)\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\u003eWhere, \u003cem\u003eα\u003c/em\u003e is the learning rate for this process. The loss function used for training the DDQN, is given via Eq.\u0026nbsp;9,\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabj\" border=\"1\"\u003e \u003ccolgroup cols=\"2\"\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 \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:L\\left(\\theta\\:\\right)=E\\left[{\\left(\\delta\\:t\\right)}^{2}\\right]\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026hellip;(9)\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 loss is minimized to optimize the model\u0026rsquo;s predictive performance levels. The fusion of VARMAx and DDQN concludes in the prediction module, where the final predicted stock value \u003cem\u003eY\u003c/em\u003e\u0026rsquo; is obtained using the optimized parameters for different use cases. The output of the model for each stock sample \u003cem\u003esi\u003c/em\u003e​ is a predicted value \u003cem\u003ey\u003c/em\u003e\u0026rsquo;​\u003cem\u003eI\u003c/em\u003e​, thereby completing the process from input data collection to final stock value prediction process. This fusion of VARMAx with DDQN, articulated through a series of complex equations, establishes a robust, dynamic, and highly precise framework for predicting stock value patterns. The methodology underscores the model\u0026rsquo;s unique capability to adapt to and accurately forecast market dynamics, setting a new benchmark in the realm of financial analytics.\u003c/p\u003e \u003cp\u003eThe following section of this paper discusses an example use case for this procedure, followed by a detailed performance analysis of the suggested model in comparison to existing techniques.\u003c/p\u003e \u003cp\u003eSample Case Study\u003c/p\u003e \u003cp\u003eThe intricate process of stock value prediction using the DQVPSVP model involves several critical stages, each contributing distinctively to the model's overall efficacy.\u003c/p\u003e \u003cp\u003eThis narrative unfolds through three primary phases: Data Collection, VARMAx processing, and the application of Deep Dyna Q Network (DDQN) optimized VARMAx.\u003c/p\u003e \u003cp\u003eInitially, the model embarks on the Data Collection phase, where it acquires actual stock values. This stage is crucial as it forms the empirical backbone of the entire predictive process. Consider a set of network requests that retrieves stock samples from a specific market. The Table \u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e represents a snippet of such collected data samples.\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\u003eSample Snippet of data samples\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=\"char\" char=\"\u0026minus;\" 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 \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStock ID\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDate\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eOpening Price\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eHighest Price\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eLowest Price\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eClosing Price\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eVolume\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eJIO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026minus;\" colname=\"c2\"\u003e \u003cp\u003e2024-01-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e150.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e155.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e149.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e154.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e1,000,000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eJIO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026minus;\" colname=\"c2\"\u003e \u003cp\u003e2024-01-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e154.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e156.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e153.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e155.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e1,200,000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eJIO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026minus;\" colname=\"c2\"\u003e \u003cp\u003e2024-01-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e155.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e157.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e154.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e156.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e1,500,000\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 data is foundational, providing the raw inputs from which sophisticated analyses are derived for different use cases. Next, the model transitions to the VARMAx phase, where it applies a sophisticated algorithm to analyze the temporal relationships inherent in the stock data samples. The VARMAx model, utilizing its capacity to handle multiple time series and incorporate exogenous factors, yields an initial set of predictions. The Table \u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e illustrates these predictive outputs:\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\u003ePredictive outputs\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=\"\u0026minus;\" 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\u003eStock ID\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDate\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePredicted Closing Price (VARMAx)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eJIO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026minus;\" colname=\"c2\"\u003e \u003cp\u003e2024-01-04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e156.9\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eJIO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026minus;\" colname=\"c2\"\u003e \u003cp\u003e2024-01-05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e157.3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eJIO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026minus;\" colname=\"c2\"\u003e \u003cp\u003e2024-01-06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e157.8\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\u003eThese predictions, while insightful, are further refined in the subsequent phase.\u003c/p\u003e \u003cp\u003eIn the final stage, the DDQN Optimized VARMAx, the model leverages the DDQN algorithm's capacity for hyperparameter optimization. This enhances the model's predictive accuracy by dynamically adjusting to the stock's volatility and market trends. The Table \u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e showcases the refined predictive outputs post-DDQN optimization:\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\u003eRefined Predictive outputs post-DDQN optimization\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=\"\u0026minus;\" 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\u003eStock ID\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDate\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePredicted Closing Price (DDQN Optimized VARMAx)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eJIO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026minus;\" colname=\"c2\"\u003e \u003cp\u003e2024-01-04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e157.1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eJIO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026minus;\" colname=\"c2\"\u003e \u003cp\u003e2024-01-05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e157.6\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eJIO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026minus;\" colname=\"c2\"\u003e \u003cp\u003e2024-01-06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e158.2\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\u003eThe progression from initial data collection, through the VARMAx predictive phase, to the DDQN-optimized predictions represents a journey from raw data to refined, actionable insights. Each step in this process adds layers of complexity and precision, ultimately rendering the model not just a predictive tool but a sophisticated analytical apparatus capable of navigating the complexities of financial markets with remarkable acumen for different value sets.\u003c/p\u003e"},{"header":"3 Result Analysis and Comparisons","content":"\u003cp\u003eIn the proposed research, the innovative fusion of the Vector Autoregressive Moving Average with eXogenous inputs (VARMAx) framework and the Deep Dyna Q algorithm represents a ground breaking shift in stock value prediction methodology. At the heart of this approach lies the strategic use of technical indicators as primary parameters, which are adeptly integrated with global indices, serving as exogenous factors in the VARMAx process. This integration forms a robust foundation, adept at capturing the intricate dependencies inherent in stock values and patterns. The VARMAx model, known for its econometric rigor, is thereby enhanced to handle the multifaceted nature of financial markets with heightened accuracy. Complementing this, the Deep Dyna Q algorithm emerges as a critical component in this architecture, dynamically tuning the hyperparameters of the VARMAx model. Its deployment signifies a leap in the adaptability of the prediction model, enabling it to continuously adjust to varying stock types and market conditions. This adaptive mechanism is not just a mere adjustment but a comprehensive recalibration of the model's predictive capabilities, ensuring that the predictions remain precise and relevant across different market scenarios. The empirical validation of this model, conducted through rigorous testing on diverse datasets from the Indian and USA stock markets, further underscores its efficacy and adaptability levels.\u003c/p\u003e \u003cp\u003eThe model is assessed using evaluation parameters such as Precision (P), Accuracy (A), Recall (R), Delay, AUC and Specificity (Sp). Based on this analysis, the precision achieved during stock value prediction operations is compared with LightGBM [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e], Graph Evolution Recurrent Unit (GERU) [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e], and FinGAT [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e], as highlighted in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn the analysis of various numbers of test stock samples (NTS), the DQVPSVP model consistently outperforms other models. For example, with 12k NTS, DQVPSVP achieves a precision of 93.79%, compared to LightGBM's [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e] 84.30%, GERU's [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e] 85.63%, and FinGAT's [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]86.63%. This superiority is maintained with larger sample sizes: at 60k NTS, DQVPSVP's precision is 93.48%, versus LightGBM's 75.52%, GERU's 94.11%, and FinGAT's 81.62%. With 150k NTS, DQVPSVP achieves 94.43%, still outperforming LightGBM (84.55%), GERU (93.28%), and FinGAT (87.19%). This indicates that DQVPSVP's performance remains robust with increasing data volume, crucial for real-time financial analytics with vast and expanding datasets.\u003c/p\u003e \u003cp\u003eSimilarly, the model is evaluated for accuracy, and the comparative analysis of the models is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e below.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e shows varying accuracy across different numbers of test stock samples (NTS). Notably, some models outperform others in specific instances. For example, with 42k NTS, LightGBM achieves 92.55% accuracy, surpassing DQVPSVP's 90.28%. However, with 78k NTS, DQVPSVP excels with 94.78% accuracy, higher than LightGBM's 87.73%, GERU's 75.81%, and Fin-GAT's 81.05%. This highlights DQVPSVP's strong but context-dependent performance. DQVPSVP's varying accuracy might stem from its sophisticated Deep Dyna Q and VARMAx framework, which adapts dynamically to complex stock market dynamics. This adaptability can cause variability in accuracy, especially in rapidly changing markets. Its real-time hyperparameter tuning adjusts to different stock types and market conditions, impacting accuracy. High prediction accuracy reduces investment errors and increases profitability. The variability among models and NTS sizes underscores the importance of choosing models based on specific market conditions and data volumes. LightGBM might be more reliable in some cases, while DQVPSVP's advanced features may offer an edge in others.\u003c/p\u003e \u003cp\u003eSimilar to this, Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e represents the recall levels is as follows.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e shown above illustrates the recall levels for various models across different numbers of test stock samples (NTS). For example, with 12k NTS, DQVPSVP achieves a recall of 89.13%, significantly higher than LightGBM's 76.60% and nearly matching GERU's 89.04%. This trend continues across most NTS sizes. At 60k NTS, DQVPSVP records a recall of 92.59%, surpassing LightGBM's 89.05% and GERU's 78.53%. In real-time stock trading, a high recall rate, like DQVPSVP's, is crucial for capitalizing on profitable opportunities. It ensures the model captures significant positive stock movements, providing timely insights and reducing the risk of missed opportunities, which is vital in fast-paced trading environments. DQVPSVP's consistent recall performance across various sample sizes indicates its robustness and scalability. This is critical in the financial domain, where data volumes and transaction numbers can be immense. A model that maintains high recall rates across different data volumes ensures comprehensive and accurate market coverage.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe delay required for the prediction procedure is visualized in a similar manner in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e as follows. Analyzing delay data for various models, including LightGBM, GERU, FinGAT, and DQVPSVP, across different numbers of test stock samples (NTS) reveals significant insights. The DQVPSVP model consistently demonstrates lower delay times compared to the other models. For example, at 12k NTS, DQVPSVP shows a delay of 121.15 ms, significantly lower than LightGBM's 156.78 ms, GERU's 145.84 ms, and FinGAT's 136.96 ms. This pattern persists at 72k NTS, with DQVPSVP recording a delay of 125.04 ms, compared to LightGBM's 161.90 ms, GERU's 162.39 ms, and FinGAT's 150.07 ms. The lower delay in DQVPSVP can be attributed to its efficient integration of the Deep Dyna Q algorithm with the VARMAx framework, enabling faster processing and prediction times. This efficiency is crucial in stock market scenarios, where real-time data processing and quick decision-making are paramount. In high-frequency trading environments, even a small delay can result in missed opportunities or substantial financial losses due to rapid stock price fluctuations.\u003c/p\u003e \u003cp\u003eSimilarly, the AUC levels can be observed from Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e as follows.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe DQVPSVP model consistently shows high AUC values across various NTS sizes, indicating superior stock movement classification. For instance, at 12k NTS, DQVPSVP achieves an AUC of 85.62%, surpassing LightGBM's 78.78%, GERU's 82.04%, and FinGAT's 76.42%. At 150k NTS, DQVPSVP's AUC reaches 98.22%, significantly outperforming the other models. This high AUC performance is due to DQVPSVP's advanced integration of the Deep Dyna Q algorithm with the VARMAx framework, enabling effective differentiation between true positive and true negative predictions. In real-time financial scenarios, a high AUC value instills confidence in predictive outputs, aiding investors and traders in making informed decisions. DQVPSVP's consistent high AUC across different data sizes demonstrates its robustness and effectiveness in diverse market conditions. In the volatile financial markets, maintaining high predictive accuracy is essential for various use cases.\u003c/p\u003e \u003cp\u003eSimilarly, the Specificity levels can be observed from Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e as follows,\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAt 12k NTS, DQVPSVP achieves an 82.19% specificity, outperforming LightGBM's 78.95%, GERU's 75.22%, and FinGAT's 75.41%. This trend continues at 102k NTS, where DQVPSVP reaches 95.66%, surpassing LightGBM's 84.78%, GERU's 83.68%, and FinGAT's 80.62%. DQVPSVP's higher specificity is due to its integration of the Deep Dyna Q algorithm with the VARMAx framework, which improves its ability to identify true negative stock movements and minimize false positives. This high specificity is crucial in financial trading, as it reduces the risk of misinterpreting stock trends, thus aiding traders and investors in making more accurate decisions.\u003c/p\u003e"},{"header":"4 Conclusion and Future Work","content":"\u003cp\u003eThe DQVPSVP model, an innovative amalgamation of the Vector Autoregressive Moving Average with eXogenous inputs (VARMAx) framework and the Deep Dyna Q algorithm, has demonstrated exceptional proficiency in predicting real-time changes in stock value patterns. Empirical tests on Indian and USA markets show significant improvements: 3.5% in precision, 2.9% in accuracy, 3.9% in recall, 4.5% in Area Under Curve (AUC), and 3.4% in specificity as compared to the existing models like LightGBM[\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e], GERU[\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e], and FinGAT[\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. Additionally, it reduces response delay by 1.5%, crucial for timely financial decisions. The implications of these results are substantial. For practitioners in the financial sector, the DQVPSVP model offers a more reliable and efficient tool for stock market analysis, paving the way for more informed investment strategies and risk management. Future work could extend the application of the DQVPSVP model to other financial instruments like bonds, commodities, and cryptocurrencies. This expansion would evaluate the model's versatility and applicability across different market dynamics. Integrating the model into real-time trading systems could offer actionable insights and enable automated trading, marking a significant advancement towards AI-driven financial decision-making. Additionally, incorporating more sophisticated technical indicators and exploring alternative data sources, such as social media sentiment and economic indicators, could further enhance the model's predictive capabilities.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003eWe declare that there is no conflict in the manuscript. The authors declare that they have no conflict of interest.\u003c/p\u003e\u003cp\u003e \u003ch2\u003e \u003cb\u003eAuthors' contributions\u003c/b\u003e \u003c/h2\u003e \u003cp\u003eRachna Sable contributed to the study conception and design, data collection, data analysis, interpretation, and manuscript drafting. Rachna Sable, Sudhanshu Gupta, and Pallavi Parlewar reviewed, validated the results and all authors approved the final manuscript.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eFunding:\u003c/h2\u003e \u003cp\u003eThere is no Funding received for this work.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eWang S (2023) A stock price prediction method based on BILSTM and improved transformer. IEEE Access 11:104211\u0026ndash;104223. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1109/access.2023.3296308\u003c/span\u003e\u003cspan address=\"10.1109/access.2023.3296308\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMu G, Gao N, Wang Y, Li D (2023) A stock price prediction model based on investor sentiment and optimized deep learning. 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Existing methods still struggle with the complex dynamics of markets, especially in adapting to stock fluctuations' multifaceted nature. In response to these limitations, the proposed work introduces a ground-breaking approach that integrates the robust forecasting capabilities of VARMAx with the adaptive ability of Deep Dyna Q algorithms. The rationale for this integration is rooted in the quest to enhance the responsiveness and accuracy of stock value predictions. The model's performance was evaluated using datasets from the Indian and USA markets. It showed significant improvements in precision, accuracy, recall, AUC, and specificity, as well as a substantial reduction in response time. These enhancements are crucial for financial decision-making, where accuracy and timeliness are essential.\u003c/p\u003e","manuscriptTitle":"Designing an efficient Deep Dyna Q based VARMAx Model for Prediction of Real-Time changes in Stock Value Patterns","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-01-13 09:53:36","doi":"10.21203/rs.3.rs-5794220/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":"ff1e3e23-373f-4b52-9782-d93c7de38e20","owner":[],"postedDate":"January 13th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-01-16T14:08:44+00:00","versionOfRecord":[],"versionCreatedAt":"2025-01-13 09:53:36","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5794220","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5794220","identity":"rs-5794220","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}