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 forecasting, we extend the comparison to neural predictors and find ARIMA still superior. We therefore propose the Autoregressive-Weight-Enhanced Kolmogorov-Arnold Network (AR-KAN), which integrates a pre-trained AR module for temporal memory with a KAN for nonlinear representation. The AR module preserves essential temporal features while reducing redundancy. Experiments demonstrate that AR-KAN matches ARIMA on almost-periodic functions and achieves the best results on $72\%$ of Rdatasets series, with a clear advantage on data with periodic structure. These results highlight AR-KAN as a robust and effective framework for time series forecasting.