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TimeKAN: KAN-based Frequency Decomposition Learning Architecture for Long-term Time Series Forecasting

Songtao Huang, Zhen Zhao, Can Li, Lei Bai

TL;DR

TimeKAN tackles long-term time series forecasting by explicitly decoupling multi-frequency components through a Decomposition-Learning-Mixing pipeline. It combines Cascaded Frequency Decomposition (CFD) to obtain per-frequency representations with a novel Multi-order KAN (M-KAN) that uses Chebyshev polynomial-based univariate functions of increasing order, and Frequency Mixing to reconstruct the original format before forecasting with a linear head. The approach leverages hierarchical preprocessing via moving averages and FFT-based frequency handling to model frequency-specific temporal patterns with lightweight parameters, achieving state-of-the-art results on several real-world datasets while remaining computationally efficient. Empirically, TimeKAN shows strong performance across multiple horizons, with ablations confirming the value of frequency upsampling, multi-order KANs, and depthwise convolution, and a notable improvement when longer look-back windows provide richer frequency information.

Abstract

Real-world time series often have multiple frequency components that are intertwined with each other, making accurate time series forecasting challenging. Decomposing the mixed frequency components into multiple single frequency components is a natural choice. However, the information density of patterns varies across different frequencies, and employing a uniform modeling approach for different frequency components can lead to inaccurate characterization. To address this challenges, inspired by the flexibility of the recent Kolmogorov-Arnold Network (KAN), we propose a KAN-based Frequency Decomposition Learning architecture (TimeKAN) to address the complex forecasting challenges caused by multiple frequency mixtures. Specifically, TimeKAN mainly consists of three components: Cascaded Frequency Decomposition (CFD) blocks, Multi-order KAN Representation Learning (M-KAN) blocks and Frequency Mixing blocks. CFD blocks adopt a bottom-up cascading approach to obtain series representations for each frequency band. Benefiting from the high flexibility of KAN, we design a novel M-KAN block to learn and represent specific temporal patterns within each frequency band. Finally, Frequency Mixing blocks is used to recombine the frequency bands into the original format. Extensive experimental results across multiple real-world time series datasets demonstrate that TimeKAN achieves state-of-the-art performance as an extremely lightweight architecture. Code is available at https://github.com/huangst21/TimeKAN.

TimeKAN: KAN-based Frequency Decomposition Learning Architecture for Long-term Time Series Forecasting

TL;DR

TimeKAN tackles long-term time series forecasting by explicitly decoupling multi-frequency components through a Decomposition-Learning-Mixing pipeline. It combines Cascaded Frequency Decomposition (CFD) to obtain per-frequency representations with a novel Multi-order KAN (M-KAN) that uses Chebyshev polynomial-based univariate functions of increasing order, and Frequency Mixing to reconstruct the original format before forecasting with a linear head. The approach leverages hierarchical preprocessing via moving averages and FFT-based frequency handling to model frequency-specific temporal patterns with lightweight parameters, achieving state-of-the-art results on several real-world datasets while remaining computationally efficient. Empirically, TimeKAN shows strong performance across multiple horizons, with ablations confirming the value of frequency upsampling, multi-order KANs, and depthwise convolution, and a notable improvement when longer look-back windows provide richer frequency information.

Abstract

Real-world time series often have multiple frequency components that are intertwined with each other, making accurate time series forecasting challenging. Decomposing the mixed frequency components into multiple single frequency components is a natural choice. However, the information density of patterns varies across different frequencies, and employing a uniform modeling approach for different frequency components can lead to inaccurate characterization. To address this challenges, inspired by the flexibility of the recent Kolmogorov-Arnold Network (KAN), we propose a KAN-based Frequency Decomposition Learning architecture (TimeKAN) to address the complex forecasting challenges caused by multiple frequency mixtures. Specifically, TimeKAN mainly consists of three components: Cascaded Frequency Decomposition (CFD) blocks, Multi-order KAN Representation Learning (M-KAN) blocks and Frequency Mixing blocks. CFD blocks adopt a bottom-up cascading approach to obtain series representations for each frequency band. Benefiting from the high flexibility of KAN, we design a novel M-KAN block to learn and represent specific temporal patterns within each frequency band. Finally, Frequency Mixing blocks is used to recombine the frequency bands into the original format. Extensive experimental results across multiple real-world time series datasets demonstrate that TimeKAN achieves state-of-the-art performance as an extremely lightweight architecture. Code is available at https://github.com/huangst21/TimeKAN.

Paper Structure

This paper contains 34 sections, 21 equations, 2 figures, 9 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Kolmogorov-Arnold Network
  4. Time Series Forecasting
  5. Time Series Decomposition
  6. TimeKAN
  7. Overall Architecture
  8. Hierarchical Sequence Preprocessing
  9. Cascaded Frequency Decomposition
  10. Multi-order KAN Representation Learning
  11. Depthwise Convolution
  12. Multi-order KANs
  13. Frequency Mixing
  14. Experiments
  15. Datasets
  16. ...and 19 more sections

Figures (2)

  • Figure 1: The architecture of TimeKAN, which mainly consists of Cascaded Frequency Decomposition block, Multi-order KAN Representation Learning block, and Frequency Mixing block. Here, we divide the frequency range of the time series into three frequency bands as an example.
  • Figure 2: Comparison of forecasting performance between TimeKAN and other three models with varying look-back windows on ETTm2 and Weather datasets. The look-back windows are selected to be $T \in \{48, 96, 192, 336, 512, 720\}$, and the prediction length is fixed to $F =96$.