HiPPO-KAN: Efficient KAN model for Time Series Analysis

SangJong Lee, Jin-Kwang Kim, JunHo Kim, TaeHan Kim, James Lee

Keywords: Time Series Forecasting, Kolmogorov-Arnold Network (KAN), Parameter Efficiency, Long-Term Dependencies, Coefficient-Based Loss Function, Lagging Problem, Financial Time Series Analysis, Nonlinear Dynamics

Abstract: In this study, we introduce a parameter-efficient model that outperforms traditional models in time series forecasting, by integrating High-order Polynomial Projection (HiPPO) theory into the Kolmogorov-Arnold network (KAN) framework. This HiPPO-KAN model achieves superior performance on long sequence data without increasing parameter count. Experimental results demonstrate that HiPPO-KAN maintains a constant parameter count while varying window sizes, in contrast to KAN, whose parameter count increases linearly with window size. Surprisingly, although the HiPPO-KAN model keeps a constant parameter count as increasing window size, it significantly outperforms KAN model at larger window sizes. These results indicate that HiPPO-KAN offers significant parameter efficiency and scalability advantages for time series forecasting. Additionally, we address the lagging problem commonly encountered in time series forecasting models, where predictions fail to promptly capture sudden changes in the data. By modifying the loss function to compute the Mean Squared Error (MSE) directly on the coefficient vectors in the HiPPO domain, we effectively resolve the lagging problem, resulting in predictions that closely follow the actual time series data. By incorporating HiPPO theory into KAN, this study showcases an efficient approach for handling long sequences with improved predictive accuracy, offering practical contributions for applications in large-scale time series data.

Submission Number: 8