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

Researchers propose AR-KAN, a neural network combining autoregressive models with Kolmogorov-Arnold Networks for improved time series forecasting. The model addresses limitations of traditional deep learning approaches by integrating temporal memory preservation with nonlinear function approximation, demonstrating superior performance on both synthetic and real-world datasets.

AR-KAN represents a meaningful advancement in time series forecasting architecture by bridging the gap between classical statistical methods and modern neural approaches. The research builds on an important empirical finding: ARIMA models consistently outperform large language models for temporal prediction tasks, suggesting that domain-specific inductive biases matter more than raw model capacity. Rather than abandoning traditional methods, the authors integrate autoregressive principles directly into a neural framework, creating a hybrid system that preserves temporal dependencies while gaining nonlinear expressiveness through Kolmogorov-Arnold Networks.

The theoretical contribution proves that AR-KAN's approximation error bound is tighter than standard KAN architecture, providing formal justification for the design choice. This matters because time series forecasting powers critical infrastructure across finance, energy systems, and supply chains. Current neural approaches often struggle with almost-periodic signals common in real-world data, where frequencies don't align neatly—a problem AR-KAN specifically addresses.

For the machine learning community, this work validates a broader principle: successful architectures often combine historical insights with contemporary methods rather than replacing one with another. The approach suggests that embedding statistical priors into deep learning frameworks yields better generalization than end-to-end learning from scratch. Practitioners deploying forecasting systems may find AR-KAN valuable for applications where both accuracy and interpretability matter, such as financial predictions or infrastructure monitoring where understanding failure modes is crucial.

• →AR-KAN integrates autoregressive temporal memory with Kolmogorov-Arnold Networks to improve time series prediction accuracy
• →Theoretical analysis proves AR-KAN has lower approximation error bounds compared to standard KAN architecture
• →The model successfully handles almost-periodic signals with non-commensurate frequencies common in real-world data
• →Research validates that combining classical statistical methods with neural networks outperforms pure deep learning approaches
• →Code is publicly available, enabling adoption across forecasting applications in finance and infrastructure monitoring