TimeKAN: an adaptive frequency-decomposed Kolmogorov–Arnold network for long-term stock forecasting

Real-world time series typically contain multiple intertwined frequency components, which poses significant challenges for accurate time series forecasting. Traditional methods adopt unified modeling strategies for different frequency components, often failing to fully capture the distinctive characteristics of each frequency component, resulting in limited prediction accuracy. Inspired by the powerful function approximation capability of Kolmogorov-Arnold Networks (KAN), this paper proposes TimeKAN, a KAN-based frequency decomposition learning architecture specifically designed for long-term time series forecasting. TimeKAN consists of three core components: the Cascading Frequency Decomposition (CFD) block employs a data-driven adaptive strategy to decompose complex multi-frequency signals into multiple relatively pure frequency band sequences; the Multi-order KAN representation learning (M-KAN) block utilizes learnable activation functions based on Chebyshev polynomials to perform specialized modeling for specific temporal patterns within each frequency band; the frequency mixing block intelligently fuses information from different frequency bands through multi-head attention mechanisms to generate final prediction results. Extensive experiments on four stock datasets (Amazon, NVIDIA, Tesla, and Apple) demonstrate that TimeKAN achieves an average improvement of 21.5% in RMSE compared to state-of-the-art baseline methods, with [Formula: see text] scores consistently exceeding 91% and significantly improved investment returns, fully validating its superior prediction performance and practical application value. Systematic ablation experiments further reveal the contribution mechanisms of each component, with the M-KAN block being the most prominent. This research contributes a novel technical approach for the time series forecasting field, showing promising potential of KAN architecture in complex sequence modeling.