Kolmogorov-Arnold Networks for Time Series Forecasting: Architectures, Implementation, and Evaluation

Kolmogorov-Arnold Networks (KANs) represent a promising direction for time series forecasting, offering theoretical advantages and growing empirical support. This paper reviews the current state of KAN-based forecasting, examining achievements, limitations, and future research opportunities. KANs provide notable advantages through spline-parametrized learnable activation functions that enhance both learning capability and model interpretability, though practical deployment presents challenges that require careful consideration. Our systematic review covers 26 distinct KAN-based architectures developed between April 2024 and the present, including foundational approaches (Basic KAN, TKAN), advanced innovations (TimeKAN, KANMixer, P-KAN), hybrid architectures (C-KAN, GCN-KAN, Fourier-KAN-Mamba), and efficiency-optimized variants (HiPPO-KAN, TaylorKAN). We provide detailed technical analysis of architectural components and implementation specifics not documented elsewhere. Beyond architectural review, we analyze KAN interpretability mechanisms including symbolic regression capabilities that distinguish KANs from traditional neural networks, and provide systematic comparisons with transformer-based, RNN-based, and linear forecasting methods. KANs perform competitively on standard benchmarks while offering substantially better interpretability, with particular strengths in compositionally-structured and moderate-dimensional multivariate scenarios. We conclude with a research framework emphasizing rigorous evaluation methodology, fair comparative studies, and systematic exploration of optimal application domains.