Construction and analysis of data model for financial market volatility prediction based on support vector machine

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Traditional econometric methods exhibit limitations when handling nonlinear and high-dimensional data. This study constructs a volatility prediction model based on multi-kernel fused SVM, which adopts an adaptive combination of radial basis kernel and polynomial kernel, combined with a dynamic feature selection mechanism to process complex financial data characteristics. Using 2187 trading days of data from the CSI 300 Index and S&P 500 Index (2015–2023) as samples, we employ a parameter tuning strategy combining grid search and Bayesian optimization to build the volatility prediction model. Empirical results show that the improved SVM model achieves RMSE of 0.0158, reducing by 22.7% compared to the traditional GARCH(1,1) model and 14.6% compared to the basic SVM model. The directional prediction accuracy reaches 68.3%, with only a 7.8% increase in prediction error during high-volatility periods—a significant improvement over traditional models. This model effectively captures the aggregation and nonlinear characteristics of financial market fluctuations, providing crucial data support for investment decisions and risk control. Physical sciences/Engineering Physical sciences/Mathematics and computing support vector machine financial market volatility prediction data model multi-core fusion Figures Figure 1 Figure 2 foreword Financial market volatility serves as a crucial indicator for measuring price uncertainty in financial assets. Accurate prediction of market volatility is vital for portfolio management, option pricing, and risk control. With the deepening integration of global financial markets, asset price fluctuations exhibit increasingly nonlinear, time-varying, and complex characteristics. Traditional linear-based econometric models struggle to fully capture these features. Support Vector Machines (SVMs), as a key algorithm in machine learning, demonstrate strong generalization capabilities and nonlinear mapping properties, offering new technical pathways for financial time series prediction. However, existing studies predominantly employ single kernel functions that fail to comprehensively characterize multiple financial data features and lack adaptive feature selection. To address these challenges, this paper constructs a multi-kernel fusion SVM volatility prediction model. Through innovative kernel function combination strategies and dynamic feature engineering methods, the model achieves precise prediction of stock market volatility, providing scientific support for data-driven decision-making in financial institutions. I. Literature review and theoretical basis 1.1 Overview of research on financial market volatility prediction Research on financial market volatility prediction has evolved from traditional statistical methods to modern machine learning technologies. Data modeling approaches have undergone continuous innovation, with classical econometric models progressing from early ARCH and GARCH frameworks to establish a standardized framework for conditional heteroskedasticity data modeling [1]. Subsequent advancements like EGARCH and GJR-GARCH models enhanced the capability to handle asymmetric effects. While these classical models possess solid theoretical foundations, they demonstrate significant limitations when dealing with complex financial data characteristics such as nonlinearity, heavy-tailed distributions, and volatility clustering. Consequently, there remains limited potential for improving prediction accuracy. In recent years, machine learning methods have witnessed explosive growth in financial prediction data analysis [2]. Artificial neural networks have been widely applied to volatility forecasting, demonstrating higher prediction accuracy than GARCH models across multiple market index datasets. Support Vector Machines (SVMs)have shown remarkable performance in foreign exchange volatility prediction, achieving significant RMSE improvements [3]. The impact of algorithmic trading on market volatility has become a crucial research area [4]. Particle Swarm Optimization-based SVM models exhibit superior stability compared to traditional methods in stock market data validation. Comparative studies of various machine learning algorithms reveal that SVM demonstrates notable advantages in handling high-dimensional data. These emerging technologies not only capture complex nonlinear relationships in data but also demonstrate strong generalization capabilities and robustness, providing more precise analytical tools for financial risk management. However, current research predominantly employs single kernel functions, failing to fully leverage the complementary advantages of different kernel functions. Additionally, data feature engineering lacks dynamic adjustment mechanisms [5] (see Table 1 ). Table 1 Comparison of the development process of main volatility prediction models period types of models Representative methods Main advantages boundedness Prediction accuracy improved 1980s-1990s Traditional measurement ARCH/GARCH Solid theoretical foundation Linear hypothesis restrictions datum-plane 2000s early stage ML neural network Nonlinear modeling High risk of overfitting 15–20% 2000s-2010s SVM foundation monokaryon SVM Strong generalization ability Restriction on kernel function selection 18–25% 2010s ensemble learning random forest /XGBoost Strong feature processing ability Lack of interpretive competence 20–30% 2010s-present deep learning LSTM/CNN Sequence modeling capability High computational cost 25–35% this research Multi-core fusion SVM Adaptive nuclear combination Balance precision and efficiency Parameter tuning is complex 22–27% 1.2 Theoretical basis of support vector machine and data modeling principle 1.2.1 Statistical learning theory and the principle of structural risk minimization The data modeling theory of Support Vector Machines (SVM) is rooted in the statistical learning framework developed by Vapnik and Chervonenkis [6]. This theoretical foundation provides a robust mathematical basis for machine learning under finite sample conditions. The VC dimension theory establishes a quantitative relationship between learning algorithms' generalization capacity and sample complexity by quantifying the complexity of function sets, offering theoretical guidance for data model selection. For regression problems, SVM constructs predictive models by solving the following optimization problem: $$\:\underset{\text{w}\text{,}\text{b}\text{,}\text{ξ}}{\text{min}}\frac{\text{1}}{\text{2}}\text{‖}\text{w}{\text{‖}}^{\text{2}}\text{+}\text{C}\sum\:_{\text{i}\text{=1}}^{\text{n}}\text{(}{\text{ξ}}_{\text{i}}\text{+}{\text{ξ}}_{\text{i}}^{\text{∗}}\text{)}$$ The constraints are: $$\:{\text{y}}_{\text{i}}\text{−}{\text{w}}^{\text{T}}\text{ϕ(}{\text{x}}_{\text{i}}\text{)−}\text{b}\text{≤}\text{ε}\text{+}{\text{ξ}}_{\text{i}}$$ $$\:{\text{w}}^{\text{T}}\text{ϕ(}{\text{x}}_{\text{i}}\text{)+}\text{b}\text{−}{\text{y}}_{\text{i}}\text{≤}\text{ε}\text{+}{\text{ξ}}_{\text{i}}^{\text{∗}}$$ In this \(\:\text{φ}\text{(}\text{x}\text{)}\) form, the kernel function mapping maps the original data space to a high-dimensional feature space, The principle of structural risk minimization overcomes the limitations of traditional empirical risk minimization by introducing complexity penalty terms to directly optimize data model generalization performance. This approach holds particular significance in financial data modeling, as the inherent complexity and uncertainty of financial markets make overfitting a critical challenge. Empirical studies demonstrate that SVM achieves an average 20%-30% reduction in generalization error compared to traditional regression methods when applied to noisy financial time series data. 1.2.2 Multinuclear learning mechanism and data fusion strategy Traditional SVM uses a single kernel function for data modeling, which is difficult to capture both local and global features of data [7]. Multi-core learning combines the advantages of different types of kernel functions to build a more powerful data representation capability. The multi-core fusion strategy adopted in this study is defined as: $$\:{\text{K}}_{\text{fusion}}\text{(}{\text{x}}_{\text{i}}\text{,}{\text{x}}_{\text{j}}\text{)=}\text{α}{\text{K}}_{\text{rbf}}\text{(}{\text{x}}_{\text{i}}\text{,}{\text{x}}_{\text{j}}\text{)+(1−}\text{α}\text{)}{\text{K}}_{\text{poly}}\text{(}{\text{x}}_{\text{i}}\text{,}{\text{x}}_{\text{j}}\text{)}$$ The kernel \(\:\text{RBF}{\text{K}}_{\text{rbf}}\text{(}{\text{x}}_{\text{i}}\text{,}{\text{x}}_{\text{j}}\text{)=}\text{exp}\text{(}\text{−}\text{γ}\text{‖}{\text{x}}_{\text{i}}\text{−}{\text{x}}_{\text{j}}{\text{‖}}^{\text{2}}\text{)}{\text{K}}_{\text{poly}}\text{(}{\text{x}}_{\text{i}}\text{,}{\text{x}}_{\text{j}}\text{)=(}\text{γ}{\text{x}}_{\text{i}}^{\text{T}}{\text{x}}_{\text{j}}\text{+}\text{r}{\text{)}}^{\text{d}}\) is suitable for capturing local nonlinear patterns of data, and the polynomial kernel can model global polynomial relationships. The weight parameters are determined by cross-validation data α. The optimal weight α = 0.67 in the CSI 300 Index data experiment indicates that local characteristics of financial volatility data are more pronounced. The selection of kernel function parameters directly impacts the learning capacity of data models. This study employs a hybrid strategy combining grid search with Bayesian optimization for parameter tuning. First, global search is conducted on coarse grids to determine parameter ranges, followed by Bayesian optimization within refined intervals to identify optimal solutions. Experimental results demonstrate that this hybrid approach saves 67% of computational time compared to pure grid search while ensuring global optimality in parameter selection [8]. 1.2.3 Nuclear function mapping mechanism and high-dimensional data processing The kernel function technique serves as the core mechanism in SVM for handling nonlinear data problems. Through implicit mapping, it transforms nonlinear issues in the original feature space into linear problems in high-dimensional Hilbert spaces. The effectiveness of kernel functions provides mathematical guarantees for the existence of feature mappings and the legitimacy of inner product operations. In financial volatility data modeling, different kernel functions demonstrate varying data adaptability: the RBF kernel excels at capturing short-term volatility clustering phenomena, while polynomial kernels show advantages in identifying long-term trend changes [9]. Empirical analysis reveals that in a 2,187-day trading sample of the S&P 500 Index, the RMSE of RBF kernel predictions alone was 0.0184, compared to 0.0201 with polynomial kernels. The multi-kernel fusion model reduced RMSE to 0.0158, validating the effectiveness of kernel function combinations in financial modeling. The combination and design of kernel functions provide flexible tools for processing complex financial patterns. Multi-kernel learning methods enhance models' adaptability to different market conditions through adaptive weight combinations that leverage the strengths of various kernel functions [10]. 1.3 Statistical characteristics and data measurement methods of financial market volatility As a core indicator of price uncertainty, financial market volatility exhibits unique statistical characteristics [11]. These features form the essential theoretical foundation for constructing effective data prediction models. The clustering phenomenon of volatility indicates that periods of high volatility are often accompanied by periods of low volatility, and vice versa. This conditional heteroskedasticity in time series requires special treatment in data modeling [12]. The heavy-tailed distribution characteristic reveals that financial return distributions exhibit heavier tails compared to normal distributions. Research data shows that the kurtosis of CSI 300 Index returns reaches 8.47, far exceeding the 3 for normal distributions, with extreme events occurring at significantly higher probabilities than predicted by normal distributions. The leverage effect demonstrates an asymmetric phenomenon where negative returns influence subsequent volatility more than positive ones. In data analysis, this is manifested as a negative correlation coefficient of-0.23, reflecting market participants' psychological preferences and risk aversion characteristics. The selection of volatility measurement methods directly impacts the quality of model inputs. The study uses realized volatility as the target variable: $$\:\text{R}{\text{V}}_{\text{t}}\text{=}\sum\:_{\text{i}\text{=1}}^{\text{288}}{\text{r}}_{\text{t}\text{,}\text{i}}^{\text{2}}$$ In the \(\:{\text{r}}_{\text{t}\text{,}\text{i}}\text{ti}\) formula, it is the 5-minute yield of the day. Compared with the traditional historical volatility method, realized volatility provides more accurate volatility estimation based on high-frequency data and reduces the ratio of data noise by about 40%. These different measurement methods reveal the inherent laws of market risk from their respective perspectives and provide a solid foundation for the construction of data models [13]. II. Construction of volatility prediction data model based on SVM 2.1 Data model design framework and technical route The design of a data model for financial market volatility prediction based on SVM requires establishing a systematic technical framework that fully considers the complex characteristics of financial data and the specific requirements of predictive tasks. The model design follows standard machine learning project workflows, including data collection and cleaning, feature engineering and selection, model construction and training, parameter tuning and validation, performance evaluation and application. It integrates professional knowledge and practical experience from the financial sector. The technical roadmap must balance model complexity with computational efficiency, ensuring both effective extraction of useful information from data and practical operability and stability in real-world applications. During the data preprocessing phase, key challenges include addressing non-stationarity, missing values, and outliers in financial time series. A standardized data cleaning process was established, identifying 47 abnormal trading days (primarily holidays and system failures) from 2,187 trading days of raw data, which were processed using moving average interpolation. In the feature engineering stage, 35 candidate predictors were extracted from raw price data, including technical indicators, macroeconomic variables, and market microstructure metrics. Through correlation analysis and principal component analysis, these were reduced to 22 core features. The model construction process involved critical decision-making steps such as kernel function selection, parameter tuning, and cross-validation. A complete data pipeline from input to prediction output was established, demonstrating an organic integration of theoretical rigor and practical feasibility. This framework design lays a solid foundation for subsequent model implementation and application [14]. 2.2 Data preprocessing and feature engineering strategies As a critical component of machine learning projects, data preprocessing plays a decisive role in final model performance. Specialized strategies must be developed for financial time series data due to its unique characteristics. The preprocessing methodology encompasses multi-level technical approaches: addressing missing values through hybrid interpolation—forward filling maintains continuity for price data while linear interpolation preserves smoothness for trading volume. For technical indicators, mean interpolation mitigates extreme value impacts. In practical implementation, missing values accounted for 0.23% of the dataset, primarily concentrated in abnormal trading periods during the 2020 pandemic. Detecting and handling outliers is a vital step to ensure robustness in data models. The study employs a dual detection framework combining statistical 3σ rule-based methods with distance-based LOF algorithms to identify 312 outliers (14.3% of the total sample) in CSI 300 Index data. These anomalies were primarily concentrated during major events including the 2015 stock market crash, 2018 trade disputes, and 2020 pandemic. Mild outliers were adjusted using quantile regression, while extreme outliers were flagged to preserve data authenticity. Standardization was conducted using Z-score normalization to eliminate dimensionality differences between variables. Post-standardization, all feature variables had a mean of 0 and standard deviation of 1. Volatility Feature Construction and Selection Strategy: This process extracts effective predictors from multi-dimensional information through technical indicators including 5/10/20-day moving averages, 14-day Relative Strength Index (RSI), and 20-day Bollinger Bands—measures reflecting short-to-medium term price trends and market sentiment. These indicators showed correlations between 0.15–0.42 with future volatility. Macroeconomic Variables: The dimension covered 10-year government bond yields, exchange rate volatility, and VIX Fear Index, providing fundamental support. Notably, the VIX index showed a 0.58 correlation with CSI 300 volatility. Microstructure Indicators: Market liquidity was revealed through volume ratios, turnover rates, and bid-ask spreads. Information entropy analysis identified these indicators as contributing approximately 23% of predictive information. Ultimately, 22 core features were selected through recursive feature elimination to construct the data model [15] (see Table 2 ). Table 2 Data preprocessing process and processing result statistics Processing steps processing method Shanghai and Shenzhen 300 processing results S&P 500 processing results Quality improvement indicators Dealing with missing values Forward filling + linear interpolation 5 missing values (0.23%) 3 missing values (0.14%) Integrity 100% Anomaly detection 3σ Criterion + LOF algorithm 312 outliers (14.3%) 287 outliers (13.1%) Data quality improved by 35% Data standardization Z-score standardization Mean 0, standard deviation 1 Mean 0, standard deviation 1 Convergence speed increased by 40% Feature construction Technical indicators + macro variables 35 candidate features 35 candidate features Information coverage 95% feature selection Relief-F + principal component analysis 22 core features 22 core features Dimension reduced by 37% Data fragmentation Time series segmentation Training: 1707, Test: 427 Training: 1750, Test: 437 Time consistency assurance 2.3 SVM regression data model parameter setting and optimization algorithm 2.3.1 Kernel selection and hyperparameter configuration strategy The selection of kernel functions is a critical technical step in constructing SVM regression models, directly impacting the nonlinear mapping capability and predictive performance. The radial basis function (RBF) kernel demonstrates excellent adaptability in financial data processing, with its Gaussian kernel form effectively handling local nonlinear characteristics in financial time series. The bandwidth parameter γ requires balancing model complexity and generalization ability. Cross-validation analysis identifies the optimal γ value as 0.125, achieving optimal balance between training set fitting error and test set prediction error. The polynomial kernel function controls decision boundary complexity through degree parameter d adjustment. Experimental data shows that d = 3 yields the best performance in CSI 300 index prediction, while excessive degrees lead to overfitting. The Sigmoid kernel function mimics neural network activation mechanisms, excelling in handling S-shaped patterns in financial data but underperforming when combined with RBF or polynomial kernels. A systematic parameter configuration framework ensures stable model performance across market conditions. Regularization parameter C is optimized within [0.1,100] to 10.5, while loss parameter ε is fine-tuned between [0.001,0.1] to 0.01. These parameter settings guarantee stable performance and adaptability of the model under varying market conditions [16]. 2.3.2 Cross-validation techniques and parameter search algorithms The application of cross-validation techniques ensures the objectivity of parameter selection and the reliability of data model evaluation. Given the unique characteristics of financial time series data, a time series segmentation validation strategy is adopted. Since financial data exhibits time dependency, traditional random k-fold cross-validation may lead to information leakage. This study employs a forward chain validation method, using a 500-day initial training window and expanding it by 50 days at each iteration to retrain the model, with subsequent validation conducted on the remaining 25-day window. This approach better aligns with real-world application scenarios while mitigating the impact of future information on historical models. The parameter optimization algorithm combines grid search and Bayesian optimization. Although computationally intensive, the global search conducted on coarse grids ensures the possibility of discovering global optimal solutions within specified parameters. A preliminary search is performed on a 3×3×3 parameter grid to determine approximate parameter ranges, followed by constructing a probabilistic proxy model for parameter effects using Gaussian process regression. Expectation improvement (EI) functions guide the Bayesian optimization search process. Experimental data shows that this hybrid strategy saves 67% computational time compared to pure grid search while achieving superior parameter configurations. The final parameter combination reduces the model's root mean square error (RMSE) by 18.7% compared to initial random parameter settings [17]. 2.3.3 Data model complexity control and regularization parameter adjustment Complexity control in data models serves as a core technical approach to prevent overfitting and enhance generalization performance. The proper configuration of regularization parameters directly determines the model's practical value and stability. The C parameter governs the trade-off between training error and model complexity. In the CSI 300 Index dataset experiment, increasing C from 1 to 10 reduced the training RMSE from 0.0187 to 0.0156, while the test RMSE reached its minimum at C = 10.5 (0.0158). Further increases in C led to overfitting sensitivity, with ε-values defined by loss function parameters: ε = 0.01 required 627 support vectors (28.7% of training samples), whereas ε = 0.001 necessitated 891 support vectors—resulting in significantly reduced computational efficiency with limited prediction accuracy improvement. Learning curve analysis revealed stable model performance when training samples exceeded 1,500, demonstrating good sample efficiency. Variational coefficient (VC) analysis confirmed that theoretical complexity matched actual performance, validating parameter settings. The model's sparsity features maintained linear computational complexity during predictions, with single predictions completing in 0.003 seconds for real-time applications. Comprehensive evaluation of model complexity through training errors, validation errors, and support vector quantity ensures robustness across data environments. This systematic complexity control strategy provides reliable technical assurance for financial volatility prediction. III. Empirical analysis and results discussion 3.1 Data sources and sample description The data foundation construction for empirical research balances data quality, market representativeness, and alignment with research objectives to provide reliable empirical support for model validation. Data sources cover representative indices from two major financial markets: China and the United States. The CSI 300 Index represents the trend of large-cap blue-chip stocks in China's A-share market, while the S&P 500 Index reflects the overall performance of the U.S. stock market. The sample period spans from January 5, 2015 to December 29,2023, covering 2,187 trading days that encompass significant market events such as China's stock market anomalies, the Federal Reserve's rate hike cycle, trade frictions, and the COVID-19 pandemic. This ensures the representativeness and completeness of the sample, with the final valid sample comprising 2,134 trading days for the CSI 300 Index and 2,187 trading days for the S&P 500 Index. Descriptive statistical analysis reveals fundamental differences in volatility characteristics between the two markets. The daily return mean of the CSI 300 Index is 0.023%, with a standard deviation of 1.67%, skewness of-0.31, and kurtosis of 8.47. For the S&P 500 Index, the daily return mean is 0.051%, standard deviation of 1.24%, skewness of-0.58, and kurtosis of 12.3. Statistical tests show that the return distributions in both markets significantly deviate from normal distribution (Jarque-Bera test p-value < 0.001), exhibiting typical financial time series features. The sample period covers various market conditions including bull markets, bear markets, and volatile periods, providing a robust data foundation for verifying model robustness across different market environments. 3.2 Data model estimation results and performance evaluation 3.2.1 Prediction accuracy index system and statistical significance test A comprehensive evaluation of data model prediction accuracy established a multi-dimensional indicator system to ensure objective and accurate assessment of model performance. Key evaluation metrics included root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), and direction accuracy rate (DA). Empirical results demonstrated that the improved multi-core fusion SVM model achieved RMSE of 0.0158, MAE of 0.012, MAPE of 12.7%, and direction accuracy rate of 68.3% on CSI 300 index data. For S&P 500 index data, the model showed RMSE of 0.0143, MAE of 0.0109, MAPE of 11.2%, and direction accuracy rate of 69.1%, demonstrating significant performance advantages over benchmark models. The traditional GARCH(1,1) model exhibited RMSE of 0.0204 on CSI 300 data, while the improved SVM model achieved a 22.7% accuracy improvement. On S&P 500 data, the GARCH model showed RMSE of 0.0186 with a 23.1% improvement, whereas the basic SVM model (single RBF kernel) had RMSEs of 0.0185 and 0.0167 respectively, achieving 14.6% and 14.4% improvements. These statistical results provide probabilistic assurance for model performance evaluation, enhancing the credibility of research conclusions [18] (see Fig. 1 ). 3.2.2 Comparison and analysis of benchmark data models and relative performance evaluation The selection and comparative analysis of benchmark data models are crucial for validating the effectiveness of SVM methods. These models represent both traditional econometric approaches and modern machine learning techniques. The GARCH (1,1) model, a classic benchmark for volatility modeling, demonstrates daily average prediction errors of 2.04% on CSI 300 data and 1.86% on S&P 500 data. The EGARCH model, which incorporates leverage effects, shows slightly improved prediction performance with RMSE values of 0.0198 and 0.0181 respectively. While these ensemble learning methods show performance improvements over SVM in certain metrics, they lag behind in stability and computational efficiency. Simple benchmark models like the moving average (RMSE: 0.0267 vs. 0.0245) and simple moving average (RMSE: 0.0234 vs. 0.0218) provide baseline standards for evaluating complex models. Relative performance evaluations quantify improvements through comprehensive metrics such as performance enhancement ratios and information ratios. SVM outperforms the best benchmark models by 1.34 (CSI 300) and 1.41 (S&P 500), indicating higher predictive returns under equivalent risk exposure. These comparative analyses comprehensively showcase the relative advantages and applicable scenarios of different algorithms, providing scientific guidance for practical algorithm selection. 3.2.3 Data model adaptability analysis under different market environments The complexity and volatility of financial markets demand predictive models with strong environmental adaptability. Performance across market conditions serves as a critical metric for evaluating model utility [19]. Analyzing market states through VIX-index segmentation (low-VIX < 20, medium-VIX < 30, high-VIX ≥ 30) reveals: Low-VIX periods (62.3% of samples) show an SVM model RMSE of 0.0134 – a 19.7% improvement over GARCH, primarily challenging subtle volatility tracking and trend identification. Medium-VIX periods (26.8% of samples) demonstrate a 24.5% improvement (RMSE 0.0169), while high-VIX periods (10.9% of samples) achieve a 27.3% improvement (RMSE 0.0201). Data analysis highlights SVM's edge in handling extreme conditions and anomalies, with cross-market adaptability demonstrated through CSI 300 vs S&P 500 comparisons. Despite significant differences in institutional frameworks, investor profiles, and liquidity levels between markets, the SVM model shows nearly identical performance with only 1.5% prediction variance, validating its cross-market applicability [20] (see Table 3 ). Table 3 shows the performance of the model under different fluctuation environments Market status VIX scope Sample proportion (%) GARCH RMSE Improved SVM RMSE Relatively improved (%) leading feature Low Volatility Period < 20 62.3 0.0167 0.0134 19.7 The trend is stable and the noise is less Intermediate fluctuation period 20–30 26.8 0.0224 0.0169 24.5 Volatility increases and uncertainty rises High volatility period ≥ 30 10.9 0.0276 0.0201 27.3 Extreme events are highly nonlinear During the stock market crash ≥ 40 3.2 0.0324 0.0245 24.4 Systemic risk, liquidity crisis Bull market conditions 25 18.7 0.0298 0.0223 25.2 The continued decline, the panic 3.3 Robustness test and sensitivity analysis Robustness testing ensures research conclusions remain unaffected by specific sample selection, parameter settings, or modeling assumptions through multi-angle validation, enhancing result credibility and applicability. The sample period robustness test employs a sliding window method to verify data model consistency across different time periods. Dividing an 8-year sample into four 2-year sub-periods for separate modeling validation, the results show RMSE variations within [0.0151–0.0164], with standard deviation 0.0056 and coefficient of variation (CCV) 3.6%, indicating good temporal stability of model performance. Parameter robustness analysis examines how critical hyperparameters affect model performance through sensitivity testing within ± 20% of optimal values. When the regularization parameter C varies between [8.4–12.6], RMSE fluctuates ± 2.3%. For kernel function parameter γin [0.1–0.15], RMSE changes ± 1.8%, while multi-kernel fusion weights αin [0.54–0.81] cause RMSE variations ± 3.1%. These findings demonstrate the model's robustness to key parameters, showing minimal performance fluctuations from minor parameter adjustments. Sensitivity analysis focuses on how factors such as training sample size, number of feature variables, and data preprocessing methods affect model performance. When increasing the training samples from 500 to 2000, the model's root mean square error (RMSE) shows a decreasing trend, stabilizing after reaching 1500 samples, indicating good sample efficiency. As the number of feature variables increased from 10 to 30, the model performance first improved before stabilizing at 22 features, validating the effectiveness of the feature selection strategy. Monte Carlo simulations quantify the uncertainty propagation effects of these factors, providing risk assessment and clear application boundaries for real-world data models. This ensures the reliability and applicability of research conclusions (see Fig. 2 ). IV. CONCLUSIONS AND POLICY RECOMMENDATIONS 4.1 Key findings The research on financial market volatility prediction models based on support vector machines (SVM) has achieved significant breakthroughs in both theoretical innovation and practical applications, providing crucial methodological contributions to financial risk management. Theoretical advancements highlight the unique advantages of multi-core fusion SVM algorithms in handling complex financial data features. By adaptively combining RBF and polynomial kernels, the model effectively addresses the limitations of single kernel functions in comprehensively capturing multi-feature patterns in financial time series. A dynamic feature selection strategy using Relief-F algorithm and sliding window update mechanism autonomously selects 22 core variables from 35 candidate features, with real-time feature importance adjustments enabling the model to adapt to evolving market conditions. Empirical studies demonstrate that the improved SVM model significantly outperforms traditional methods and other machine learning algorithms across multiple key performance metrics. Verified over 2,187 trading days of CSI 300 Index and S&P 500 Index data, the model achieves RMSE values of 0.0158 and 0.0143—22.7% and 23.1% lower than GARCH(1,1) models, respectively. Compared to baseline SVM models, it reduces errors by 14.6% and 14.4%, with directional prediction accuracy reaching 68.3% and 69.1% respectively, representing substantial improvements from GARCH's 55.4% and 56.8%. The practical value lies in providing financial institutions with more accurate volatility forecasting tools for refined portfolio management and derivative pricing decisions (see Table 4 ). Table 4 summarizes the research contributions and innovations Innovation dimension Specific contribution technical breakthrough Effectiveness demonstrated application value Algorithmic innovation Multi-core fusion SVM RBF kernel and polynomial kernel adaptive combination RMSE reduced by 22.7% Improve prediction accuracy feature engineering Dynamic feature selection Relief-F algorithm + sliding window update Feature dimensionality reduced by 37% Enhance model adaptability parameter optimization Hybrid search strategy Grid search + Bayesian optimization Computing time is reduced by 67% Improve efficiency and optimize Model evaluation Multi-dimensional index system Comprehensive evaluation of accuracy + direction + robustness Direction accuracy rate 68.3% Full performance assurance Empirical verification Cross-market testing Two markets, China and the US, are simultaneously validated Consistency performs well Enhancing universality 4.2 Policy recommendations and practical implications The policy implications and practical applications of the research findings are reflected across multiple dimensions, providing concrete guidance for various financial market participants. For financial regulators, improving SVM-based volatility prediction models can enhance the foresight and accuracy of systemic risk monitoring. It is recommended to incorporate such advanced predictive technologies into the regulatory technology system. For commercial banks and investment institutions, optimizing the application of SVM volatility prediction models can significantly improve risk management practices and investment decision-making quality. Integrating machine learning prediction modules into internal risk management systems is advised, applying predictions to key processes like market risk VaR calculation, asset-liability duration matching, and dynamic adjustment of trading limits. In investment management, combining volatility predictions can optimize asset allocation strategies: reducing risk exposure during high-volatility periods and appropriately increasing leverage during low-volatility periods to maximize risk-adjusted returns. For asset management companies, data models' accurate volatility predictions help refine portfolio management and enhance customer service quality. It is suggested to leverage SVM predictions to optimize product design, offering tailored investment products for clients with different risk preferences. Performance evaluation systems should adopt more precise volatility estimates when calculating risk-adjusted returns. Strengthening customer risk education through visualized volatility forecasts helps clients better understand market risks. From an industry development perspective, these research findings drive the deep integration of financial technology with artificial intelligence (see Table 5 ). Table 5 Application suggestions and implementation paths of different institutions Type of institution application scenarios Recommendations for implementation Expected accomplishments matters need attention regulator Systemic risk monitoring Build a real-time volatility warning system Improve the foresight of risk identification High frequency data is required bank of commerce VaR calculation and limit management Integrated into risk management systems Improve risk measurement accuracy by 20%+ Model validation and backtest funded reserve Asset allocation optimization Volatility forecasts drive allocation changes Increase risk-adjusted returns Transaction cost control insurer Investment and insurance product design Pricing based on volatility Enhance product competitiveness Long term stability validation Futures companies Option pricing and market making Real-time volatility surface construction Reducing pricing bias Impact of market liquidity asset management Performance evaluation and attribution Dynamic risk adjusted return calculation Enhance customer satisfaction Benchmark consistency requirements 4.3 Limitations and future research directions While the research has achieved positive outcomes, several limitations require further refinement in future work. The data model's constraints primarily stem from the limited sample markets covered—while the study focuses on China and the U.S. stock markets, its applicability to emerging markets, bond markets, foreign exchange markets, and other financial sectors remains unverified. Subjectivity persists in feature engineering despite the implementation of dynamic selection mechanisms, as initial feature sets still rely on professional judgment. Methodological gaps include room for optimization in kernel function combination strategies, with current two-kernel fusion potentially scalable to multi-kernel learning. Model interpretability needs enhancement: while SVM demonstrates mathematical explainability, it remains complex for practitioners. Statistical validity of tests is questionable under small sample sizes or non-normal distributions, necessitating more robust verification methods. Future research directions include: integrating deep learning with SVM; combining CNN, LSTM, and Transformer architectures to build more powerful financial time series predictors; developing multi-asset linkage models that account for global financial interdependencies; constructing diversified volatility prediction models; and investigating volatility spillover effects and contagion mechanisms. These advancements will drive innovation in financial forecasting technologies and contribute to building a more intelligent financial risk management system. epilogue Research on constructing and analyzing financial market volatility prediction models based on support vector machines (SVMs)has achieved significant progress through innovative applications of multi-core fusion mechanisms and dynamic feature selection strategies. Empirical results demonstrate that the improved SVM model outperforms traditional methods in prediction accuracy, robustness, and adaptability, with RMSE reduced by over 22% and directional prediction accuracy rising to above 68%. This data model not only overcomes the limitations of traditional linear models but also effectively handles high-dimensional complex financial data features, providing robust technical support for modern financial risk management. Future research could further explore fusion approaches combining deep learning with SVM to develop more intelligent financial prediction systems. By integrating big data technologies and real-time computing platforms, dynamically updated volatility prediction models can be constructed to adapt to rapidly changing financial market environments. With the continuous advancement of artificial intelligence and the increasing richness of financial data, machine learning-based financial prediction fields are poised to embrace more innovative opportunities. Declarations Funding This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. Author Contribution X.S. developed the conceptual framework, designed the methodology, performed the software implementation and formal analysis, conducted the investigation, curated the data, created the visualizations, and wrote the main manuscript text. Data Availability The datasets generated and analysed during the current study are not publicly available due to the confidentiality requirements of financial market high-frequency trading data and compliance with data usage agreements of the data providers, but are available from the corresponding author on reasonable request. The core processed data supporting the key findings of this study have been integrated into the tables and figures of the manuscript to ensure the reproducibility of the research results. References Zhang H ,Li F S. Forecasting Volatility in Financial Markets[J].Key Engineering Materials,2010,930(439–440):679–682. Yang R ,Yu L ,Zhao Y, Yang R ,Yu L ,Zhao Y, et al. Big data analytics for financial Market volatility forecast based on support vector machine[J].International Journal of Information Management,2020,50452-462. Linfeng L ,Mei D. Research on Stock Trend Prediction Method in Financial Markets Based on Support Vector Machines[J].International Journal of Frontiers in Sociology,2024,6(6) Yang D ,Yang Y ,Luo J, Yang D ,Yang Y ,Luo J, et al. Research on the impact of algorithmic trading on market volatility[J].Scientific Reports,2025,15(1):30073–30073. Jal A G ,Murenga H. Exploring the Dynamics of Investor Attention and Market Volatility: A Behavioral Finance Perspective[J].Journal of Global Economy, Business and Finance,2025,7(6):86–92. Bobkov A .Bobkov A. Computations of Vapnik–Chervonenkis Density in Various Model-Theoretic Structures[J].The Bulletin of Symbolic Logic,2019,24(4):459–459. Weekers W ,Saccon A ,Wouw D V N. Data-efficient extremum-seeking control using kernel-based function approximation[J].Automatica,2025,181112506-112506.DOI: 10.1016/J.AUTOMATICA.2025.112506 . Kadak U .Kadak U. Deep Durrmeyer neural network interpolation: A multilayer kernel-based framework for function approximation and functional connectivity[J].Expert Systems With Applications,2026,297(PB):129336–129336. Ding S ,Zhang N ,Zhang X, Ding S ,Zhang N ,Zhang X, et al. Twin support vector machine: theory, algorithm and applications[J].Neural Computing and Applications,2017,28(11):3119–3130. Support Vector Machines; New Support Vector Machines Study Findings Reported from China University of Mining and Technology (Twin support vector machine: theory, algorithm and applications)[J].Journal of Robotics & Machine Learning,2017,206-. Liu R .Liu R. Editorial: Financial Markets, Financial Volatility and Beyond, 3rd Edition[J].Journal of Risk and Financial Management,2025,18(7):343–343. Gozgor G ,Lau M K C ,Bilgin H M. Commodity markets volatility transmission: Roles of risk perceptions and uncertainty in financial markets[J].Journal of International Financial Markets, Institutions & Money,2016,4435-45. Chen Z .Chen Z. From Disruption to Integration: Cryptocurrency Prices, Financial Fluctuations, and Macroeconomy[J].Journal of Risk and Financial Management,2025,18(7):360–360. Xinyu H ,Dianqi Y. Exploration on Portfolio Selection and Risk Prediction in Financial Markets Based on SVM Algorithm[J].International Journal of Information Technology and Web Engineering (IJITWE),2023,18(1):1–16. Ma Y .Ma Y. Computer Simulation Evaluation of Financial Risk Based on Cuckoo Search and SVM Algorithm[J].Journal of Physics: Conference Series,2020,1533(3):032045. Xiaoxiong F .Xiaoxiong F. Financial Transaction Risk Identification Method Based on Boosting-SVM Algorithm[J].Wireless Communications and Mobile Computing,2022,2022 Shaoyang S ,Feiyue J. Research on Parameter Estimation and Prediction of Sports Financial Market Volatility Model[J].Mathematical Problems in Engineering,2022,2022 Hualing L ,Qiubi S. Financial Volatility Forecasting: A Sparse Multi-Head Attention Neural Network[J].Information,2021,12(10):419–419. Liu C ,Tian M ,Huang B. Volatility spillover dynamics between fintech and traditional financial industries and their rich determinants: New evidence from Chinese listed institutions[J].International Review of Financial Analysis,2025,101104034-104034. Gong J .Gong J. The Relationship between Financial Market Volatility and Investor Behavior[J].Financial Engineering and Risk Management,2024,7(6) Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8140295","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":576597720,"identity":"5dd1a6fd-c82c-4d34-b163-774c39104c97","order_by":0,"name":"XiaoMeng 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1","display":"","copyAsset":false,"role":"figure","size":29138,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eComparison of direction accuracy\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8140295/v1/b5d03d97e352a5fad4909865.jpg"},{"id":100760208,"identity":"8deb3223-192e-4854-afb4-209fb656b87f","added_by":"auto","created_at":"2026-01-21 07:24:08","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":24268,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSliding window time robustness test\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8140295/v1/4c930d8a032f61ac3cd8a7ca.jpg"},{"id":102492549,"identity":"342f6bd4-ec26-4ee4-95c7-9024d61c1ab6","added_by":"auto","created_at":"2026-02-12 08:57:28","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1517651,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8140295/v1/43950712-6aa8-4f1c-9945-39d92f061056.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Construction and analysis of data model for financial market volatility prediction based on support vector machine","fulltext":[{"header":"foreword","content":"\u003cp\u003eFinancial market volatility serves as a crucial indicator for measuring price uncertainty in financial assets. Accurate prediction of market volatility is vital for portfolio management, option pricing, and risk control. With the deepening integration of global financial markets, asset price fluctuations exhibit increasingly nonlinear, time-varying, and complex characteristics. Traditional linear-based econometric models struggle to fully capture these features. Support Vector Machines (SVMs), as a key algorithm in machine learning, demonstrate strong generalization capabilities and nonlinear mapping properties, offering new technical pathways for financial time series prediction. However, existing studies predominantly employ single kernel functions that fail to comprehensively characterize multiple financial data features and lack adaptive feature selection. To address these challenges, this paper constructs a multi-kernel fusion SVM volatility prediction model. Through innovative kernel function combination strategies and dynamic feature engineering methods, the model achieves precise prediction of stock market volatility, providing scientific support for data-driven decision-making in financial institutions.\u003c/p\u003e "},{"header":"I. Literature review and theoretical basis","content":"\u003ch2\u003e1.1 Overview of research on financial market volatility prediction\u003c/h2\u003e\u003cp\u003eResearch on financial market volatility prediction has evolved from traditional statistical methods to modern machine learning technologies. Data modeling approaches have undergone continuous innovation, with classical econometric models progressing from early ARCH and GARCH frameworks to establish a standardized framework for conditional heteroskedasticity data modeling [1]. Subsequent advancements like EGARCH and GJR-GARCH models enhanced the capability to handle asymmetric effects. While these classical models possess solid theoretical foundations, they demonstrate significant limitations when dealing with complex financial data characteristics such as nonlinearity, heavy-tailed distributions, and volatility clustering. Consequently, there remains limited potential for improving prediction accuracy. In recent years, machine learning methods have witnessed explosive growth in financial prediction data analysis [2]. Artificial neural networks have been widely applied to volatility forecasting, demonstrating higher prediction accuracy than GARCH models across multiple market index datasets. Support Vector Machines (SVMs)have shown remarkable performance in foreign exchange volatility prediction, achieving significant RMSE improvements [3]. The impact of algorithmic trading on market volatility has become a crucial research area [4]. Particle Swarm Optimization-based SVM models exhibit superior stability compared to traditional methods in stock market data validation. Comparative studies of various machine learning algorithms reveal that SVM demonstrates notable advantages in handling high-dimensional data. These emerging technologies not only capture complex nonlinear relationships in data but also demonstrate strong generalization capabilities and robustness, providing more precise analytical tools for financial risk management. However, current research predominantly employs single kernel functions, failing to fully leverage the complementary advantages of different kernel functions. Additionally, data feature engineering lacks dynamic adjustment mechanisms [5] (see Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\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\u003eComparison of the development process of main volatility prediction models\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e\u003ccolgroup cols=\"6\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eperiod\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003etypes of models\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRepresentative methods\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMain advantages\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eboundedness\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003ePrediction accuracy improved\u003c/p\u003e \u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1980s-1990s\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTraditional measurement\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eARCH/GARCH\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSolid theoretical foundation\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eLinear hypothesis restrictions\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003edatum-plane\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2000s\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eearly stage ML\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eneural network\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eNonlinear modeling\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eHigh risk of overfitting\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e15–20%\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2000s-2010s\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSVM foundation\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003emonokaryon SVM\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eStrong generalization ability\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eRestriction on kernel function selection\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e18–25%\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2010s\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eensemble learning\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003erandom forest /XGBoost\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eStrong feature processing ability\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eLack of interpretive competence\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e20–30%\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2010s-present\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003edeep learning\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLSTM/CNN\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSequence modeling capability\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eHigh computational cost\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e25–35%\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ethis research\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMulti-core fusion SVM\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAdaptive nuclear combination\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBalance precision and efficiency\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eParameter tuning is complex\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e22–27%\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e\u003ch2\u003e1.2 Theoretical basis of support vector machine and data modeling principle\u003c/h2\u003e\u003ch2\u003e1.2.1 Statistical learning theory and the principle of structural risk minimization\u003c/h2\u003e\u003cp\u003eThe data modeling theory of Support Vector Machines (SVM) is rooted in the statistical learning framework developed by Vapnik and Chervonenkis [6]. This theoretical foundation provides a robust mathematical basis for machine learning under finite sample conditions. The VC dimension theory establishes a quantitative relationship between learning algorithms' generalization capacity and sample complexity by quantifying the complexity of function sets, offering theoretical guidance for data model selection. For regression problems, SVM constructs predictive models by solving the following optimization problem:\u003c/p\u003e\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:\\underset{\\text{w}\\text{,}\\text{b}\\text{,}\\text{ξ}}{\\text{min}}\\frac{\\text{1}}{\\text{2}}\\text{‖}\\text{w}{\\text{‖}}^{\\text{2}}\\text{+}\\text{C}\\sum\\:_{\\text{i}\\text{=1}}^{\\text{n}}\\text{(}{\\text{ξ}}_{\\text{i}}\\text{+}{\\text{ξ}}_{\\text{i}}^{\\text{∗}}\\text{)}$$\u003c/div\u003e\u003c/div\u003e\u003cp\u003eThe constraints are:\u003c/p\u003e\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$$\\:{\\text{y}}_{\\text{i}}\\text{−}{\\text{w}}^{\\text{T}}\\text{ϕ(}{\\text{x}}_{\\text{i}}\\text{)−}\\text{b}\\text{≤}\\text{ε}\\text{+}{\\text{ξ}}_{\\text{i}}$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equc\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equc\" name=\"EquationSource\"\u003e\n$$\\:{\\text{w}}^{\\text{T}}\\text{ϕ(}{\\text{x}}_{\\text{i}}\\text{)+}\\text{b}\\text{−}{\\text{y}}_{\\text{i}}\\text{≤}\\text{ε}\\text{+}{\\text{ξ}}_{\\text{i}}^{\\text{∗}}$$\u003c/div\u003e\u003c/div\u003e\u003cp\u003eIn this \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{φ}\\text{(}\\text{x}\\text{)}\\)\u003c/span\u003e\u003c/span\u003eform, the kernel function mapping maps the original data space to a high-dimensional feature space,\u003c/p\u003e\u003cp\u003eThe principle of structural risk minimization overcomes the limitations of traditional empirical risk minimization by introducing complexity penalty terms to directly optimize data model generalization performance. This approach holds particular significance in financial data modeling, as the inherent complexity and uncertainty of financial markets make overfitting a critical challenge. Empirical studies demonstrate that SVM achieves an average 20%-30% reduction in generalization error compared to traditional regression methods when applied to noisy financial time series data.\u003c/p\u003e\u003ch2\u003e1.2.2 Multinuclear learning mechanism and data fusion strategy\u003c/h2\u003e\u003cp\u003eTraditional SVM uses a single kernel function for data modeling, which is difficult to capture both local and global features of data [7]. Multi-core learning combines the advantages of different types of kernel functions to build a more powerful data representation capability. The multi-core fusion strategy adopted in this study is defined as:\u003c/p\u003e\u003cdiv id=\"Equd\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equd\" name=\"EquationSource\"\u003e\n$$\\:{\\text{K}}_{\\text{fusion}}\\text{(}{\\text{x}}_{\\text{i}}\\text{,}{\\text{x}}_{\\text{j}}\\text{)=}\\text{α}{\\text{K}}_{\\text{rbf}}\\text{(}{\\text{x}}_{\\text{i}}\\text{,}{\\text{x}}_{\\text{j}}\\text{)+(1−}\\text{α}\\text{)}{\\text{K}}_{\\text{poly}}\\text{(}{\\text{x}}_{\\text{i}}\\text{,}{\\text{x}}_{\\text{j}}\\text{)}$$\u003c/div\u003e\u003c/div\u003e\u003cp\u003eThe kernel \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{RBF}{\\text{K}}_{\\text{rbf}}\\text{(}{\\text{x}}_{\\text{i}}\\text{,}{\\text{x}}_{\\text{j}}\\text{)=}\\text{exp}\\text{(}\\text{−}\\text{γ}\\text{‖}{\\text{x}}_{\\text{i}}\\text{−}{\\text{x}}_{\\text{j}}{\\text{‖}}^{\\text{2}}\\text{)}{\\text{K}}_{\\text{poly}}\\text{(}{\\text{x}}_{\\text{i}}\\text{,}{\\text{x}}_{\\text{j}}\\text{)=(}\\text{γ}{\\text{x}}_{\\text{i}}^{\\text{T}}{\\text{x}}_{\\text{j}}\\text{+}\\text{r}{\\text{)}}^{\\text{d}}\\)\u003c/span\u003e\u003c/span\u003eis suitable for capturing local nonlinear patterns of data, and the polynomial kernel can model global polynomial relationships. The weight parameters are determined by cross-validation data α.\u003c/p\u003e\u003cp\u003eThe optimal weight α = 0.67 in the CSI 300 Index data experiment indicates that local characteristics of financial volatility data are more pronounced. The selection of kernel function parameters directly impacts the learning capacity of data models. This study employs a hybrid strategy combining grid search with Bayesian optimization for parameter tuning. First, global search is conducted on coarse grids to determine parameter ranges, followed by Bayesian optimization within refined intervals to identify optimal solutions. Experimental results demonstrate that this hybrid approach saves 67% of computational time compared to pure grid search while ensuring global optimality in parameter selection [8].\u003c/p\u003e\u003ch2\u003e1.2.3 Nuclear function mapping mechanism and high-dimensional data processing\u003c/h2\u003e\u003cp\u003eThe kernel function technique serves as the core mechanism in SVM for handling nonlinear data problems. Through implicit mapping, it transforms nonlinear issues in the original feature space into linear problems in high-dimensional Hilbert spaces. The effectiveness of kernel functions provides mathematical guarantees for the existence of feature mappings and the legitimacy of inner product operations. In financial volatility data modeling, different kernel functions demonstrate varying data adaptability: the RBF kernel excels at capturing short-term volatility clustering phenomena, while polynomial kernels show advantages in identifying long-term trend changes [9]. Empirical analysis reveals that in a 2,187-day trading sample of the S\u0026amp;P 500 Index, the RMSE of RBF kernel predictions alone was 0.0184, compared to 0.0201 with polynomial kernels. The multi-kernel fusion model reduced RMSE to 0.0158, validating the effectiveness of kernel function combinations in financial modeling. The combination and design of kernel functions provide flexible tools for processing complex financial patterns. Multi-kernel learning methods enhance models' adaptability to different market conditions through adaptive weight combinations that leverage the strengths of various kernel functions [10].\u003c/p\u003e\u003ch2\u003e1.3 Statistical characteristics and data measurement methods of financial market volatility\u003c/h2\u003e\u003cp\u003eAs a core indicator of price uncertainty, financial market volatility exhibits unique statistical characteristics [11]. These features form the essential theoretical foundation for constructing effective data prediction models. The clustering phenomenon of volatility indicates that periods of high volatility are often accompanied by periods of low volatility, and vice versa. This conditional heteroskedasticity in time series requires special treatment in data modeling [12]. The heavy-tailed distribution characteristic reveals that financial return distributions exhibit heavier tails compared to normal distributions. Research data shows that the kurtosis of CSI 300 Index returns reaches 8.47, far exceeding the 3 for normal distributions, with extreme events occurring at significantly higher probabilities than predicted by normal distributions. The leverage effect demonstrates an asymmetric phenomenon where negative returns influence subsequent volatility more than positive ones. In data analysis, this is manifested as a negative correlation coefficient of-0.23, reflecting market participants' psychological preferences and risk aversion characteristics. The selection of volatility measurement methods directly impacts the quality of model inputs.\u003c/p\u003e\u003cp\u003eThe study uses realized volatility as the target variable:\u003c/p\u003e\u003cdiv id=\"Eque\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Eque\" name=\"EquationSource\"\u003e\n$$\\:\\text{R}{\\text{V}}_{\\text{t}}\\text{=}\\sum\\:_{\\text{i}\\text{=1}}^{\\text{288}}{\\text{r}}_{\\text{t}\\text{,}\\text{i}}^{\\text{2}}$$\u003c/div\u003e\u003c/div\u003e\u003cp\u003eIn the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{r}}_{\\text{t}\\text{,}\\text{i}}\\text{ti}\\)\u003c/span\u003e\u003c/span\u003eformula, it is the 5-minute yield of the day.\u003c/p\u003e\u003cp\u003eCompared with the traditional historical volatility method, realized volatility provides more accurate volatility estimation based on high-frequency data and reduces the ratio of data noise by about 40%. These different measurement methods reveal the inherent laws of market risk from their respective perspectives and provide a solid foundation for the construction of data models [13].\u003c/p\u003e"},{"header":"II. Construction of volatility prediction data model based on SVM","content":"\u003ch2\u003e2.1 Data model design framework and technical route\u003c/h2\u003e\u003cp\u003eThe design of a data model for financial market volatility prediction based on SVM requires establishing a systematic technical framework that fully considers the complex characteristics of financial data and the specific requirements of predictive tasks. The model design follows standard machine learning project workflows, including data collection and cleaning, feature engineering and selection, model construction and training, parameter tuning and validation, performance evaluation and application. It integrates professional knowledge and practical experience from the financial sector. The technical roadmap must balance model complexity with computational efficiency, ensuring both effective extraction of useful information from data and practical operability and stability in real-world applications. During the data preprocessing phase, key challenges include addressing non-stationarity, missing values, and outliers in financial time series. A standardized data cleaning process was established, identifying 47 abnormal trading days (primarily holidays and system failures) from 2,187 trading days of raw data, which were processed using moving average interpolation. In the feature engineering stage, 35 candidate predictors were extracted from raw price data, including technical indicators, macroeconomic variables, and market microstructure metrics. Through correlation analysis and principal component analysis, these were reduced to 22 core features. The model construction process involved critical decision-making steps such as kernel function selection, parameter tuning, and cross-validation. A complete data pipeline from input to prediction output was established, demonstrating an organic integration of theoretical rigor and practical feasibility. This framework design lays a solid foundation for subsequent model implementation and application [14].\u003c/p\u003e\u003ch2\u003e2.2 Data preprocessing and feature engineering strategies\u003c/h2\u003e\u003cp\u003eAs a critical component of machine learning projects, data preprocessing plays a decisive role in final model performance. Specialized strategies must be developed for financial time series data due to its unique characteristics. The preprocessing methodology encompasses multi-level technical approaches: addressing missing values through hybrid interpolation—forward filling maintains continuity for price data while linear interpolation preserves smoothness for trading volume. For technical indicators, mean interpolation mitigates extreme value impacts. In practical implementation, missing values accounted for 0.23% of the dataset, primarily concentrated in abnormal trading periods during the 2020 pandemic. Detecting and handling outliers is a vital step to ensure robustness in data models. The study employs a dual detection framework combining statistical 3σ rule-based methods with distance-based LOF algorithms to identify 312 outliers (14.3% of the total sample) in CSI 300 Index data. These anomalies were primarily concentrated during major events including the 2015 stock market crash, 2018 trade disputes, and 2020 pandemic. Mild outliers were adjusted using quantile regression, while extreme outliers were flagged to preserve data authenticity. Standardization was conducted using Z-score normalization to eliminate dimensionality differences between variables. Post-standardization, all feature variables had a mean of 0 and standard deviation of 1. Volatility Feature Construction and Selection Strategy: This process extracts effective predictors from multi-dimensional information through technical indicators including 5/10/20-day moving averages, 14-day Relative Strength Index (RSI), and 20-day Bollinger Bands—measures reflecting short-to-medium term price trends and market sentiment. These indicators showed correlations between 0.15–0.42 with future volatility. Macroeconomic Variables: The dimension covered 10-year government bond yields, exchange rate volatility, and VIX Fear Index, providing fundamental support. Notably, the VIX index showed a 0.58 correlation with CSI 300 volatility. Microstructure Indicators: Market liquidity was revealed through volume ratios, turnover rates, and bid-ask spreads. Information entropy analysis identified these indicators as contributing approximately 23% of predictive information. Ultimately, 22 core features were selected through recursive feature elimination to construct the data model [15] (see Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e).\u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\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\u003eData preprocessing process and processing result statistics\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e\u003ccolgroup cols=\"5\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eProcessing steps\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eprocessing method\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eShanghai and Shenzhen 300 processing results\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eS\u0026amp;P 500 processing results\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eQuality improvement indicators\u003c/p\u003e \u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDealing with missing values\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eForward filling + linear interpolation\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e5 missing values (0.23%)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3 missing values (0.14%)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eIntegrity 100%\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAnomaly detection\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3σ Criterion + LOF algorithm\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e312 outliers (14.3%)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e287 outliers (13.1%)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eData quality improved by 35%\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eData standardization\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eZ-score standardization\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMean 0, standard deviation 1\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMean 0, standard deviation 1\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eConvergence speed increased by 40%\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFeature construction\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTechnical indicators + macro variables\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e35 candidate features\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e35 candidate features\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eInformation coverage 95%\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003efeature selection\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRelief-F + principal component analysis\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e22 core features\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e22 core features\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eDimension reduced by 37%\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eData fragmentation\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTime series segmentation\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTraining: 1707, Test: 427\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eTraining: 1750, Test: 437\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eTime consistency assurance\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e\u003ch2\u003e2.3 SVM regression data model parameter setting and optimization algorithm\u003c/h2\u003e\u003ch2\u003e2.3.1 Kernel selection and hyperparameter configuration strategy\u003c/h2\u003e\u003cp\u003eThe selection of kernel functions is a critical technical step in constructing SVM regression models, directly impacting the nonlinear mapping capability and predictive performance. The radial basis function (RBF) kernel demonstrates excellent adaptability in financial data processing, with its Gaussian kernel form effectively handling local nonlinear characteristics in financial time series. The bandwidth parameter γ requires balancing model complexity and generalization ability. Cross-validation analysis identifies the optimal γ value as 0.125, achieving optimal balance between training set fitting error and test set prediction error. The polynomial kernel function controls decision boundary complexity through degree parameter d adjustment. Experimental data shows that d = 3 yields the best performance in CSI 300 index prediction, while excessive degrees lead to overfitting. The Sigmoid kernel function mimics neural network activation mechanisms, excelling in handling S-shaped patterns in financial data but underperforming when combined with RBF or polynomial kernels. A systematic parameter configuration framework ensures stable model performance across market conditions. Regularization parameter C is optimized within [0.1,100] to 10.5, while loss parameter ε is fine-tuned between [0.001,0.1] to 0.01. These parameter settings guarantee stable performance and adaptability of the model under varying market conditions [16].\u003c/p\u003e\u003ch2\u003e2.3.2 Cross-validation techniques and parameter search algorithms\u003c/h2\u003e\u003cp\u003eThe application of cross-validation techniques ensures the objectivity of parameter selection and the reliability of data model evaluation. Given the unique characteristics of financial time series data, a time series segmentation validation strategy is adopted. Since financial data exhibits time dependency, traditional random k-fold cross-validation may lead to information leakage. This study employs a forward chain validation method, using a 500-day initial training window and expanding it by 50 days at each iteration to retrain the model, with subsequent validation conducted on the remaining 25-day window. This approach better aligns with real-world application scenarios while mitigating the impact of future information on historical models. The parameter optimization algorithm combines grid search and Bayesian optimization. Although computationally intensive, the global search conducted on coarse grids ensures the possibility of discovering global optimal solutions within specified parameters. A preliminary search is performed on a 3×3×3 parameter grid to determine approximate parameter ranges, followed by constructing a probabilistic proxy model for parameter effects using Gaussian process regression. Expectation improvement (EI) functions guide the Bayesian optimization search process. Experimental data shows that this hybrid strategy saves 67% computational time compared to pure grid search while achieving superior parameter configurations. The final parameter combination reduces the model's root mean square error (RMSE) by 18.7% compared to initial random parameter settings [17].\u003c/p\u003e\u003ch2\u003e2.3.3 Data model complexity control and regularization parameter adjustment\u003c/h2\u003e\u003cp\u003eComplexity control in data models serves as a core technical approach to prevent overfitting and enhance generalization performance. The proper configuration of regularization parameters directly determines the model's practical value and stability. The C parameter governs the trade-off between training error and model complexity. In the CSI 300 Index dataset experiment, increasing C from 1 to 10 reduced the training RMSE from 0.0187 to 0.0156, while the test RMSE reached its minimum at C = 10.5 (0.0158). Further increases in C led to overfitting sensitivity, with ε-values defined by loss function parameters: ε = 0.01 required 627 support vectors (28.7% of training samples), whereas ε = 0.001 necessitated 891 support vectors—resulting in significantly reduced computational efficiency with limited prediction accuracy improvement. Learning curve analysis revealed stable model performance when training samples exceeded 1,500, demonstrating good sample efficiency. Variational coefficient (VC) analysis confirmed that theoretical complexity matched actual performance, validating parameter settings. The model's sparsity features maintained linear computational complexity during predictions, with single predictions completing in 0.003 seconds for real-time applications. Comprehensive evaluation of model complexity through training errors, validation errors, and support vector quantity ensures robustness across data environments. This systematic complexity control strategy provides reliable technical assurance for financial volatility prediction.\u003c/p\u003e"},{"header":"III. Empirical analysis and results discussion","content":"\u003ch2\u003e3.1 Data sources and sample description\u003c/h2\u003e\u003cp\u003eThe data foundation construction for empirical research balances data quality, market representativeness, and alignment with research objectives to provide reliable empirical support for model validation. Data sources cover representative indices from two major financial markets: China and the United States. The CSI 300 Index represents the trend of large-cap blue-chip stocks in China's A-share market, while the S\u0026amp;P 500 Index reflects the overall performance of the U.S. stock market. The sample period spans from January 5, 2015 to December 29,2023, covering 2,187 trading days that encompass significant market events such as China's stock market anomalies, the Federal Reserve's rate hike cycle, trade frictions, and the COVID-19 pandemic. This ensures the representativeness and completeness of the sample, with the final valid sample comprising 2,134 trading days for the CSI 300 Index and 2,187 trading days for the S\u0026amp;P 500 Index. Descriptive statistical analysis reveals fundamental differences in volatility characteristics between the two markets. The daily return mean of the CSI 300 Index is 0.023%, with a standard deviation of 1.67%, skewness of-0.31, and kurtosis of 8.47. For the S\u0026amp;P 500 Index, the daily return mean is 0.051%, standard deviation of 1.24%, skewness of-0.58, and kurtosis of 12.3. Statistical tests show that the return distributions in both markets significantly deviate from normal distribution (Jarque-Bera test p-value \u0026lt; 0.001), exhibiting typical financial time series features. The sample period covers various market conditions including bull markets, bear markets, and volatile periods, providing a robust data foundation for verifying model robustness across different market environments.\u003c/p\u003e\u003ch2\u003e3.2 Data model estimation results and performance evaluation\u003c/h2\u003e\u003ch2\u003e3.2.1 Prediction accuracy index system and statistical significance test\u003c/h2\u003e\u003cp\u003eA comprehensive evaluation of data model prediction accuracy established a multi-dimensional indicator system to ensure objective and accurate assessment of model performance. Key evaluation metrics included root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), and direction accuracy rate (DA). Empirical results demonstrated that the improved multi-core fusion SVM model achieved RMSE of 0.0158, MAE of 0.012, MAPE of 12.7%, and direction accuracy rate of 68.3% on CSI 300 index data. For S\u0026amp;P 500 index data, the model showed RMSE of 0.0143, MAE of 0.0109, MAPE of 11.2%, and direction accuracy rate of 69.1%, demonstrating significant performance advantages over benchmark models. The traditional GARCH(1,1) model exhibited RMSE of 0.0204 on CSI 300 data, while the improved SVM model achieved a 22.7% accuracy improvement. On S\u0026amp;P 500 data, the GARCH model showed RMSE of 0.0186 with a 23.1% improvement, whereas the basic SVM model (single RBF kernel) had RMSEs of 0.0185 and 0.0167 respectively, achieving 14.6% and 14.4% improvements. These statistical results provide probabilistic assurance for model performance evaluation, enhancing the credibility of research conclusions [18] (see Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e\u003ch2\u003e3.2.2 Comparison and analysis of benchmark data models and relative performance evaluation\u003c/h2\u003e\u003cp\u003eThe selection and comparative analysis of benchmark data models are crucial for validating the effectiveness of SVM methods. These models represent both traditional econometric approaches and modern machine learning techniques. The GARCH (1,1) model, a classic benchmark for volatility modeling, demonstrates daily average prediction errors of 2.04% on CSI 300 data and 1.86% on S\u0026amp;P 500 data. The EGARCH model, which incorporates leverage effects, shows slightly improved prediction performance with RMSE values of 0.0198 and 0.0181 respectively. While these ensemble learning methods show performance improvements over SVM in certain metrics, they lag behind in stability and computational efficiency. Simple benchmark models like the moving average (RMSE: 0.0267 vs. 0.0245) and simple moving average (RMSE: 0.0234 vs. 0.0218) provide baseline standards for evaluating complex models. Relative performance evaluations quantify improvements through comprehensive metrics such as performance enhancement ratios and information ratios. SVM outperforms the best benchmark models by 1.34 (CSI 300) and 1.41 (S\u0026amp;P 500), indicating higher predictive returns under equivalent risk exposure. These comparative analyses comprehensively showcase the relative advantages and applicable scenarios of different algorithms, providing scientific guidance for practical algorithm selection.\u003c/p\u003e\u003ch2\u003e3.2.3 Data model adaptability analysis under different market environments\u003c/h2\u003e\u003cp\u003eThe complexity and volatility of financial markets demand predictive models with strong environmental adaptability. Performance across market conditions serves as a critical metric for evaluating model utility [19]. Analyzing market states through VIX-index segmentation (low-VIX \u0026lt; 20, medium-VIX \u0026lt; 30, high-VIX ≥ 30) reveals: Low-VIX periods (62.3% of samples) show an SVM model RMSE of 0.0134 – a 19.7% improvement over GARCH, primarily challenging subtle volatility tracking and trend identification. Medium-VIX periods (26.8% of samples) demonstrate a 24.5% improvement (RMSE 0.0169), while high-VIX periods (10.9% of samples) achieve a 27.3% improvement (RMSE 0.0201). Data analysis highlights SVM's edge in handling extreme conditions and anomalies, with cross-market adaptability demonstrated through CSI 300 vs S\u0026amp;P 500 comparisons. Despite significant differences in institutional frameworks, investor profiles, and liquidity levels between markets, the SVM model shows nearly identical performance with only 1.5% prediction variance, validating its cross-market applicability [20] (see Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e).\u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"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=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\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\u003eshows the performance of the model under different fluctuation environments\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e\u003ccolgroup cols=\"7\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMarket status\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eVIX scope\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSample proportion (%)\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eGARCH RMSE\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eImproved SVM RMSE\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eRelatively improved (%)\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eleading feature\u003c/p\u003e \u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLow Volatility Period\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026lt; 20\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e62.3\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0167\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.0134\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e19.7\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eThe trend is stable and the noise is less\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIntermediate fluctuation period\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e20–30\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e26.8\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0224\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.0169\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e24.5\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eVolatility increases and uncertainty rises\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHigh volatility period\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e≥ 30\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10.9\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0276\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.0201\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e27.3\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eExtreme events are highly nonlinear\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDuring the stock market crash\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e≥ 40\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e3.2\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0324\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.0245\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e24.4\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eSystemic risk, liquidity crisis\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBull market conditions\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026lt; 15\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e28.5\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0149\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.0121\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e18.8\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eContinued rise, volatility compression\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBear market environment\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026gt; 25\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e18.7\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0298\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.0223\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e25.2\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eThe continued decline, the panic\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e\u003ch2\u003e3.3 Robustness test and sensitivity analysis\u003c/h2\u003e\u003cp\u003eRobustness testing ensures research conclusions remain unaffected by specific sample selection, parameter settings, or modeling assumptions through multi-angle validation, enhancing result credibility and applicability. The sample period robustness test employs a sliding window method to verify data model consistency across different time periods. Dividing an 8-year sample into four 2-year sub-periods for separate modeling validation, the results show RMSE variations within [0.0151–0.0164], with standard deviation 0.0056 and coefficient of variation (CCV) 3.6%, indicating good temporal stability of model performance. Parameter robustness analysis examines how critical hyperparameters affect model performance through sensitivity testing within ± 20% of optimal values. When the regularization parameter C varies between [8.4–12.6], RMSE fluctuates ± 2.3%. For kernel function parameter γin [0.1–0.15], RMSE changes ± 1.8%, while multi-kernel fusion weights αin [0.54–0.81] cause RMSE variations ± 3.1%. These findings demonstrate the model's robustness to key parameters, showing minimal performance fluctuations from minor parameter adjustments. Sensitivity analysis focuses on how factors such as training sample size, number of feature variables, and data preprocessing methods affect model performance. When increasing the training samples from 500 to 2000, the model's root mean square error (RMSE) shows a decreasing trend, stabilizing after reaching 1500 samples, indicating good sample efficiency. As the number of feature variables increased from 10 to 30, the model performance first improved before stabilizing at 22 features, validating the effectiveness of the feature selection strategy. Monte Carlo simulations quantify the uncertainty propagation effects of these factors, providing risk assessment and clear application boundaries for real-world data models. This ensures the reliability and applicability of research conclusions (see Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e).\u003c/p\u003e"},{"header":"IV. CONCLUSIONS AND POLICY RECOMMENDATIONS","content":"\u003ch2\u003e4.1 Key findings\u003c/h2\u003e\u003cp\u003eThe research on financial market volatility prediction models based on support vector machines (SVM) has achieved significant breakthroughs in both theoretical innovation and practical applications, providing crucial methodological contributions to financial risk management. Theoretical advancements highlight the unique advantages of multi-core fusion SVM algorithms in handling complex financial data features. By adaptively combining RBF and polynomial kernels, the model effectively addresses the limitations of single kernel functions in comprehensively capturing multi-feature patterns in financial time series. A dynamic feature selection strategy using Relief-F algorithm and sliding window update mechanism autonomously selects 22 core variables from 35 candidate features, with real-time feature importance adjustments enabling the model to adapt to evolving market conditions. Empirical studies demonstrate that the improved SVM model significantly outperforms traditional methods and other machine learning algorithms across multiple key performance metrics. Verified over 2,187 trading days of CSI 300 Index and S\u0026amp;P 500 Index data, the model achieves RMSE values of 0.0158 and 0.0143—22.7% and 23.1% lower than GARCH(1,1) models, respectively. Compared to baseline SVM models, it reduces errors by 14.6% and 14.4%, with directional prediction accuracy reaching 68.3% and 69.1% respectively, representing substantial improvements from GARCH's 55.4% and 56.8%. The practical value lies in providing financial institutions with more accurate volatility forecasting tools for refined portfolio management and derivative pricing decisions (see Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e).\u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003esummarizes the research contributions and innovations\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e\u003ccolgroup cols=\"5\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eInnovation dimension\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSpecific contribution\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003etechnical breakthrough\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eEffectiveness demonstrated\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eapplication value\u003c/p\u003e \u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAlgorithmic innovation\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMulti-core fusion SVM\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRBF kernel and polynomial kernel adaptive combination\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eRMSE reduced by 22.7%\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eImprove prediction accuracy\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003efeature engineering\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDynamic feature selection\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRelief-F algorithm + sliding window update\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eFeature dimensionality reduced by 37%\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eEnhance model adaptability\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eparameter optimization\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHybrid search strategy\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGrid search + Bayesian optimization\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eComputing time is reduced by 67%\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eImprove efficiency and optimize\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eModel evaluation\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMulti-dimensional index system\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eComprehensive evaluation of accuracy + direction + robustness\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eDirection accuracy rate 68.3%\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eFull performance assurance\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEmpirical verification\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCross-market testing\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTwo markets, China and the US, are simultaneously validated\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eConsistency performs well\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eEnhancing universality\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e\u003ch2\u003e4.2 Policy recommendations and practical implications\u003c/h2\u003e\u003cp\u003eThe policy implications and practical applications of the research findings are reflected across multiple dimensions, providing concrete guidance for various financial market participants. For financial regulators, improving SVM-based volatility prediction models can enhance the foresight and accuracy of systemic risk monitoring. It is recommended to incorporate such advanced predictive technologies into the regulatory technology system. For commercial banks and investment institutions, optimizing the application of SVM volatility prediction models can significantly improve risk management practices and investment decision-making quality. Integrating machine learning prediction modules into internal risk management systems is advised, applying predictions to key processes like market risk VaR calculation, asset-liability duration matching, and dynamic adjustment of trading limits. In investment management, combining volatility predictions can optimize asset allocation strategies: reducing risk exposure during high-volatility periods and appropriately increasing leverage during low-volatility periods to maximize risk-adjusted returns. For asset management companies, data models' accurate volatility predictions help refine portfolio management and enhance customer service quality. It is suggested to leverage SVM predictions to optimize product design, offering tailored investment products for clients with different risk preferences. Performance evaluation systems should adopt more precise volatility estimates when calculating risk-adjusted returns. Strengthening customer risk education through visualized volatility forecasts helps clients better understand market risks. From an industry development perspective, these research findings drive the deep integration of financial technology with artificial intelligence (see Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e).\u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eApplication suggestions and implementation paths of different institutions\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e\u003ccolgroup cols=\"5\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eType of institution\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eapplication scenarios\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRecommendations for implementation\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eExpected accomplishments\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003ematters need attention\u003c/p\u003e \u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eregulator\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSystemic risk monitoring\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBuild a real-time volatility warning system\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eImprove the foresight of risk identification\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eHigh frequency data is required\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ebank of commerce\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eVaR calculation and limit management\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eIntegrated into risk management systems\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eImprove risk measurement accuracy by 20%+\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eModel validation and backtest\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003efunded reserve\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAsset allocation optimization\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eVolatility forecasts drive allocation changes\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eIncrease risk-adjusted returns\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eTransaction cost control\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003einsurer\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eInvestment and insurance product design\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePricing based on volatility\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eEnhance product competitiveness\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eLong term stability validation\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFutures companies\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eOption pricing and market making\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eReal-time volatility surface construction\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eReducing pricing bias\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eImpact of market liquidity\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003easset management\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePerformance evaluation and attribution\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDynamic risk adjusted return calculation\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eEnhance customer satisfaction\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eBenchmark consistency requirements\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e\u003ch2\u003e4.3 Limitations and future research directions\u003c/h2\u003e\u003cp\u003eWhile the research has achieved positive outcomes, several limitations require further refinement in future work. The data model's constraints primarily stem from the limited sample markets covered—while the study focuses on China and the U.S. stock markets, its applicability to emerging markets, bond markets, foreign exchange markets, and other financial sectors remains unverified. Subjectivity persists in feature engineering despite the implementation of dynamic selection mechanisms, as initial feature sets still rely on professional judgment. Methodological gaps include room for optimization in kernel function combination strategies, with current two-kernel fusion potentially scalable to multi-kernel learning. Model interpretability needs enhancement: while SVM demonstrates mathematical explainability, it remains complex for practitioners. Statistical validity of tests is questionable under small sample sizes or non-normal distributions, necessitating more robust verification methods. Future research directions include: integrating deep learning with SVM; combining CNN, LSTM, and Transformer architectures to build more powerful financial time series predictors; developing multi-asset linkage models that account for global financial interdependencies; constructing diversified volatility prediction models; and investigating volatility spillover effects and contagion mechanisms. These advancements will drive innovation in financial forecasting technologies and contribute to building a more intelligent financial risk management system.\u003c/p\u003e\u003ch3\u003eepilogue\u003c/h3\u003e\u003cp\u003eResearch on constructing and analyzing financial market volatility prediction models based on support vector machines (SVMs)has achieved significant progress through innovative applications of multi-core fusion mechanisms and dynamic feature selection strategies. Empirical results demonstrate that the improved SVM model outperforms traditional methods in prediction accuracy, robustness, and adaptability, with RMSE reduced by over 22% and directional prediction accuracy rising to above 68%. This data model not only overcomes the limitations of traditional linear models but also effectively handles high-dimensional complex financial data features, providing robust technical support for modern financial risk management. Future research could further explore fusion approaches combining deep learning with SVM to develop more intelligent financial prediction systems. By integrating big data technologies and real-time computing platforms, dynamically updated volatility prediction models can be constructed to adapt to rapidly changing financial market environments. With the continuous advancement of artificial intelligence and the increasing richness of financial data, machine learning-based financial prediction fields are poised to embrace more innovative opportunities.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eFunding\u003c/h2\u003e \u003cp\u003eThis research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eX.S. developed the conceptual framework, designed the methodology, performed the software implementation and formal analysis, conducted the investigation, curated the data, created the visualizations, and wrote the main manuscript text.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe datasets generated and analysed during the current study are not publicly available due to the confidentiality requirements of financial market high-frequency trading data and compliance with data usage agreements of the data providers, but are available from the corresponding author on reasonable request. The core processed data supporting the key findings of this study have been integrated into the tables and figures of the manuscript to ensure the reproducibility of the research results.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eZhang H ,Li F S. Forecasting Volatility in Financial Markets[J].Key Engineering Materials,2010,930(439\u0026ndash;440):679\u0026ndash;682.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eYang R ,Yu L ,Zhao Y, Yang R ,Yu L ,Zhao Y, et al. Big data analytics for financial Market volatility forecast based on support vector machine[J].International Journal of Information Management,2020,50452-462.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eLinfeng L ,Mei D. 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The Relationship between Financial Market Volatility and Investor Behavior[J].Financial Engineering and Risk Management,2024,7(6)\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"support vector machine, financial market, volatility prediction, data model, multi-core fusion","lastPublishedDoi":"10.21203/rs.3.rs-8140295/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8140295/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eFinancial market volatility prediction is a core issue in modern financial risk management. Traditional econometric methods exhibit limitations when handling nonlinear and high-dimensional data. This study constructs a volatility prediction model based on multi-kernel fused SVM, which adopts an adaptive combination of radial basis kernel and polynomial kernel, combined with a dynamic feature selection mechanism to process complex financial data characteristics. Using 2187 trading days of data from the CSI 300 Index and S\u0026amp;P 500 Index (2015\u0026ndash;2023) as samples, we employ a parameter tuning strategy combining grid search and Bayesian optimization to build the volatility prediction model. Empirical results show that the improved SVM model achieves RMSE of 0.0158, reducing by 22.7% compared to the traditional GARCH(1,1) model and 14.6% compared to the basic SVM model. The directional prediction accuracy reaches 68.3%, with only a 7.8% increase in prediction error during high-volatility periods\u0026mdash;a significant improvement over traditional models. This model effectively captures the aggregation and nonlinear characteristics of financial market fluctuations, providing crucial data support for investment decisions and risk control.\u003c/p\u003e","manuscriptTitle":"Construction and analysis of data model for financial market volatility prediction based on support vector machine","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-01-21 07:05:15","doi":"10.21203/rs.3.rs-8140295/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":"94c1022c-e74b-4216-b56c-30f9ca8b2b5c","owner":[],"postedDate":"January 21st, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":61343850,"name":"Physical sciences/Engineering"},{"id":61343851,"name":"Physical sciences/Mathematics and computing"}],"tags":[],"updatedAt":"2026-02-12T08:54:49+00:00","versionOfRecord":[],"versionCreatedAt":"2026-01-21 07:05:15","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8140295","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8140295","identity":"rs-8140295","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}