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FilterTS: Comprehensive Frequency Filtering for Multivariate Time Series Forecasting

Yulong Wang, Yushuo Liu, Xiaoyi Duan, Kai Wang

TL;DR

FilterTS tackles the challenge of forecasting with high-dimensional multivariate time series by explicitly modeling both stable and dynamically changing frequency components. It introduces a Dynamic Cross-Variable Filtering Module and a Static Global Filtering Module that operate in the frequency domain, converting time-domain convolution into efficient multiplicative operations. Through extensive experiments on eight real-world datasets, FilterTS achieves superior forecasting accuracy and reduced computational requirements, with ablations demonstrating the importance of both filtering pathways. The approach offers a scalable mechanism to leverage inter-variable frequency dependencies, delivering practical benefits in domains with many variables and diverse temporal patterns.

Abstract

Multivariate time series forecasting is crucial across various industries, where accurate extraction of complex periodic and trend components can significantly enhance prediction performance. However, existing models often struggle to capture these intricate patterns. To address these challenges, we propose FilterTS, a novel forecasting model that utilizes specialized filtering techniques based on the frequency domain. FilterTS introduces a Dynamic Cross-Variable Filtering Module, a key innovation that dynamically leverages other variables as filters to extract and reinforce shared variable frequency components across variables in multivariate time series. Additionally, a Static Global Filtering Module captures stable frequency components, identified throughout the entire training set. Moreover, the model is built in the frequency domain, converting time-domain convolutions into frequency-domain multiplicative operations to enhance computational efficiency. Extensive experimental results on eight real-world datasets have demonstrated that FilterTS significantly outperforms existing methods in terms of prediction accuracy and computational efficiency.

FilterTS: Comprehensive Frequency Filtering for Multivariate Time Series Forecasting

TL;DR

FilterTS tackles the challenge of forecasting with high-dimensional multivariate time series by explicitly modeling both stable and dynamically changing frequency components. It introduces a Dynamic Cross-Variable Filtering Module and a Static Global Filtering Module that operate in the frequency domain, converting time-domain convolution into efficient multiplicative operations. Through extensive experiments on eight real-world datasets, FilterTS achieves superior forecasting accuracy and reduced computational requirements, with ablations demonstrating the importance of both filtering pathways. The approach offers a scalable mechanism to leverage inter-variable frequency dependencies, delivering practical benefits in domains with many variables and diverse temporal patterns.

Abstract

Multivariate time series forecasting is crucial across various industries, where accurate extraction of complex periodic and trend components can significantly enhance prediction performance. However, existing models often struggle to capture these intricate patterns. To address these challenges, we propose FilterTS, a novel forecasting model that utilizes specialized filtering techniques based on the frequency domain. FilterTS introduces a Dynamic Cross-Variable Filtering Module, a key innovation that dynamically leverages other variables as filters to extract and reinforce shared variable frequency components across variables in multivariate time series. Additionally, a Static Global Filtering Module captures stable frequency components, identified throughout the entire training set. Moreover, the model is built in the frequency domain, converting time-domain convolutions into frequency-domain multiplicative operations to enhance computational efficiency. Extensive experimental results on eight real-world datasets have demonstrated that FilterTS significantly outperforms existing methods in terms of prediction accuracy and computational efficiency.
Paper Structure (43 sections, 52 equations, 5 figures, 3 tables)

This paper contains 43 sections, 52 equations, 5 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Multivariate Time Series Forecasting Models
  4. Frequency-Domain Enhanced Time Series Forecasting Models
  5. Preliminary
  6. Problem Formulation
  7. Fast Fourier Transform (FFT)
  8. Method
  9. Overall Structure
  10. Time to Frequency Embedding
  11. Dynamic Cross-Variable Filtering Module
  12. Time Series as Filter
  13. Generation of Dynamic Cross-Variable Filters
  14. Filtering Decomposition and Aggregation
  15. Static Global Filtering Module
  16. ...and 28 more sections

Figures (5)

  • Figure 1: Illustration of Stable and Synchronized Variable Frequency Components Using the ETTh1 Dataset. (a) displays the frequency spectrum of the HUFL variable across the entire training set, highlighting dominant stable frequency components with red dots. (b) shows synchronized variable frequency components between HUFL and MUFL variables within a rapidly fluctuating input window (outlined with a red rectangle), after subtracting dominant stable frequency components.
  • Figure 2: Overview of FilterTS, which comprises the following key modules: (a) the Time to Frequency Embedding Module, responsible for converting the time-domain series into the frequency domain; (b) the Dynamic Cross-Variable Filtering Module, designed to extract variable frequency components; (c) the Static Global Filtering Module, which focuses on capturing stable frequency components; and finally, (d) the Frequency to Time Projection Module, which transforms the frequency domain representation back into the time domain to generate the final predictions.
  • Figure 3: Performance Analysis of FilterTS: Assessing MSE, Training Time, and Memory Usage, evaluated on the Weather Dataset with a 96-In/336-Out Setup.
  • Figure A1: Comprehensive Performance Analysis of FilterTS: Assessing MSE, Average Training Time per Iteration during the First Epoch, and Memory Usage (lower is better) at Batch Size 32, evaluated across Various Datasets with a 96-In/336-Out Setup.
  • Figure A2: Hyper-Parameter Sensitivity Analysis of the FilterTS Model on the ETTm2 and Weather Datasets with a 96-In/336-Out Setup: (a) Impact of the $\alpha$-Quantile on model performance; (b) Effects of varying the number of global static filters (num_static_filters); (c) Influence of global static filter bandwidth (delta_bandwidth).