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AR-KAN: Autoregressive-Weight-Enhanced Kolmogorov-Arnold Network for Time Series Forecasting

Traditional neural networks struggle to capture the spectral structure of complex signals. Fourier neural networks (FNNs) attempt to address this by embedding Fourier series components, yet many real-world signals are almost-periodic with non-commensurate frequencies, posing additional challenges. Building on prior work showing that ARIMA outperforms large language models (LLMs) for time series forecasting, we extend the comparison to neural predictors and find that ARIMA still maintains a clear advantage. Inspired by this finding, we propose the Autoregressive-Weight-Enhanced Kolmogorov-Arnold Network (AR-KAN). Based in the Universal Myopic Mapping Theorem, it integrates a pre-trained AR module for temporal memory with a KAN for nonlinear representation. We prove that the AR module preserves essential temporal features while reducing redundancy, and that the upper bound of the approximation error for AR-KAN is smaller than that for KAN in a probabilistic sense. Experimental results also demonstrate that AR-KAN delivers exceptional performance compared to existing models, both on synthetic almost-periodic functions and real-world datasets. These results highlight AR-KAN as a robust and effective framework for time series forecasting. Our code is available at https://github.com/ChenZeng001/AR-KAN.

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