A Hybrid GARCH-BiLSTM-KAN Model for Crude Oil Price Forecasting: Capturing Volatility, Temporal Dependencies, and Nonlinear Dynamics

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.