This study examines volatility spillovers between Chinese and U.S. equity markets by developing a comprehensive framework that captures asymmetric volatility, extreme co-movements, and dynamic correlations. We propose an integrated methodology combining EGARCH models with Student-t innovations, a Student-t copula, and a Dynamic Conditional Correlation (DCC) structure. Using daily returns of the Hang Seng Index (HSI) and the S&P 500, our analysis reveals three principal findings. First, the EGARCH model effectively captures the pronounced leverage effect and fat-tailed distributions characteristic of both markets. Second, the Student-t copula demonstrates the best fit among competing specifications, indicating significant symmetric tail dependence between the two markets. Third, time-varying correlations exhibit high persistence, rising during crises yet remaining within a moderate range. Crucially, out-of-sample forecasting shows that our unified framework achieves superior predictive accuracy relative to standard benchmarks. These findings provide valuable insights for investors designing hedging strategies, exchanges determining margin requirements, and policymakers monitoring financial contagion. Our approach offers a robust tool for analyzing volatility transmission between developed and emerging markets.

Crude oil prices, as a cornerstone of global energy markets, exhibit intricate dynamics---including volatility clustering, asymmetric temporal dependencies, and nonlinear responses to geopolitical, economic, and supply-demand shocks---posing formidable challenges to accurate forecasting. Existing models often struggle to simultaneously capture these multifaceted characteristics, limiting their predictive robustness. To address this, this study proposes a novel hybrid framework which synergistically integrates three complementary components: (1) the Generalized Autoregressive Conditional Heteroskedasticity model to quantify time-varying volatility and address clustering effects; (2) the Bidirectional Long Short-Term Memory network to model bidirectional temporal relationships, capturing both historical and future contextual influences on price movements; and (3) the Kolmogorov-Arnold Network to refine nonlinear patterns through univariate basis functions, enhancing the mapping of complex high-dimensional dependencies beyond the capabilities of traditional neural networks. Empirical validation is conducted using 39 years of daily West Texas Intermediate crude oil prices (1986-2025), a dataset encompassing critical events such as the 2008 financial crisis, 2020 COVID-19 pandemic, and 2022 geopolitical tensions, ensuring robustness across diverse market conditions. The proposed model is rigorously compared against benchmark models, including traditional volatility models, standalone deep learning architectures, and other hybrid models. Results demonstrate that the proposed hybrid achieves superior performance with the lowest root mean squared error, mean absolute error, and the highest coefficient of determination. Statistical tests confirm the significance of its outperformance, highlighting the synergistic value of integrating volatility modeling, bidirectional sequence learning, and advanced nonlinear refinement. This research advances energy economics by providing a robust forecasting tool, with implications for policymakers in strategic energy planning, energy firms in risk hedging, and financial institutions in derivative pricing and portfolio optimization.

This study examines whether increasing architectural complexity improves forecasting accuracy in deep learning-based financial models. Using daily spot price data from the Shanghai Metals Market for copper (Cu), aluminum (Al), and zinc (Zn) spanning January 2015 to September 2025, a standardized preprocessing pipeline was applied, including z-score normalization and sliding window sequence construction (window length = 30, forecast horizon = 1). A total of eighteen models were systematically evaluated, including gated recurrent units (GRUs), long short-term memory (LSTM) networks, convolutional neural network-bidirectional LSTM-attention hybrids (CNN-BiLSTM-Attention), as well as traditional econometric models (autoregressive integrated moving average and generalized autoregressive conditional heteroskedasticity), machine learning models (random forest and extreme gradient boosting), and a Transformer-based model. All deep learning models were trained exclusively on Cu data and evaluated on independent Al and Zn datasets to assess generalizability. Results show that the standard GRU model achieves the lowest error rates (mean absolute error [MAE] = 1032.85; root mean square error = 1344.30) and highest explanatory power (coefficient of determination [R²] = 0.907) on the Cu test set, while also performing strongly on Al (MAE = 167.51, R² = 0.918) and Zn (MAE = 254.23, R² = 0.952). Ablation analysis demonstrates that adding architectural components such as attention mechanisms, bidirectional layers, and convolutional modules reduces predictive accuracy. Statistical testing using the Diebold-Mariano test indicates that most performance differences are significant (p < 0.05). These findings highlight the limitations of unnecessary model complexity and support the use of simpler, robust approaches for commodity price forecasting.

Crude oil prices exhibit complex dynamics---such as volatility clustering, asymmetric temporal dependencies, and nonlinear responses to geopolitical and economic shocks---that pose challenges to accurate forecasting. To address this, we propose a hybrid model, GBK-Net, which integrates three complementary components: GARCH for modeling time-varying volatility, BiLSTM for capturing bidirectional temporal dependencies, and Kolmogorov-Arnold Network (KAN) for refining nonlinear relationships. Empirical validation is conducted on 39 years of daily WTI crude oil prices (1986--2025), covering major events such as the 2008 financial crisis and the COVID--19 pandemic. Comparative experiments against benchmark models---including GARCH, EGARCH, LSTM, and CNN--LSTM--KAN---demonstrate that GBK-Net achieves the lowest prediction error (RMSE = 2.49; R² = 0.981), with statistical tests confirming its superiority. We also benchmark nested specifications using approximately unbiased tests [1]. This work contributes a robust forecasting tool for energy economics, with implications for strategic planning, risk hedging, and financial decision-making in volatile energy markets. Unless otherwise noted, we model and evaluate on shifted log-returns to accommodate the 2020 negative-price episode; results using arithmetic returns are reported as robustness checks in the Appendix.

1. Crude oil, as a pivotal strategic commodity, profoundly influences global economic stability, geopolitical dynamics, industrial production costs, and inflation trajectories (Hamilton 2003; Kilia...

Crude oil prices, as a cornerstone of global energy markets, exhibit intricate dynamics---including volatility clustering, asymmetric temporal dependencies, and nonlinear responses to geopolitical, economic, and supply-demand shocks---posing formidable challenges to accurate forecasting. Existing models often struggle to simultaneously capture these multifaceted characteristics, limiting their predictive robustness. To address this, this study proposes a novel hybrid framework which synergistically integrates three complementary components: (1) the Generalized Autoregressive Conditional Heteroskedasticity model to quantify time-varying volatility and address clustering effects; (2) the Bidirectional Long Short-Term Memory network to model bidirectional temporal relationships, capturing both historical and future contextual influences on price movements; and (3) the Kolmogorov-Arnold Network to refine nonlinear patterns through univariate basis functions, enhancing the mapping of complex high-dimensional dependencies beyond the capabilities of traditional neural networks. Empirical validation is conducted using 39 years of daily West Texas Intermediate crude oil prices (1986-2025), a dataset encompassing critical events such as the 2008 financial crisis, 2020 COVID-19 pandemic, and 2022 geopolitical tensions, ensuring robustness across diverse market conditions. The proposed model is rigorously compared against benchmark models, including traditional volatility models, standalone deep learning architectures, and other hybrid models. Results demonstrate that the proposed hybrid achieves superior performance with the lowest root mean squared error, mean absolute error, and the highest coefficient of determination. Statistical tests confirm the significance of its outperformance, highlighting the synergistic value of integrating volatility modeling, bidirectional sequence learning, and advanced nonlinear refinement. This research advances energy economics by providing a robust forecasting tool, with implications for policymakers in strategic energy planning, energy firms in risk hedging, and financial institutions in derivative pricing and portfolio optimization.