WPMixer: Efficient Multi-Resolution Mixing for Long-Term Time Series Forecasting

TL;DR

We introduce WPMixer, a novel MLP-mixer-based framework for long-term time series forecasting that jointly exploits time-domain and frequency-domain structure via multi-level wavelet decomposition. Each wavelet coefficient series is processed in its own resolution branch using a patching-based local encoder and a two-stage mixer (patch and embedding) to capture both local and global information, followed by reconstruction of the forecast. The approach achieves state-of-the-art or competitive accuracy on seven diverse datasets while reducing computational cost, and extensive ablations confirm the importance of decomposition depth, patching, embedding mixing, and the chosen loss. Overall, WPMixer offers a scalable, efficient alternative to transformer-based methods for long-horizon forecasting with robust performance across datasets and seeds.

Abstract

Time series forecasting is crucial for various applications, such as weather forecasting, power load forecasting, and financial analysis. In recent studies, MLP-mixer models for time series forecasting have been shown as a promising alternative to transformer-based models. However, the performance of these models is still yet to reach its potential. In this paper, we propose Wavelet Patch Mixer (WPMixer), a novel MLP-based model, for long-term time series forecasting, which leverages the benefits of patching, multi-resolution wavelet decomposition, and mixing. Our model is based on three key components: (i) multi-resolution wavelet decomposition, (ii) patching and embedding, and (iii) MLP mixing. Multi-resolution wavelet decomposition efficiently extracts information in both the frequency and time domains. Patching allows the model to capture an extended history with a look-back window and enhances capturing local information while MLP mixing incorporates global information. Our model significantly outperforms state-of-the-art MLP-based and transformer-based models for long-term time series forecasting in a computationally efficient way, demonstrating its efficacy and potential for practical applications.

Figures (3)

• Figure 1: WPMixer with $m$ levels of wavelet decomposition. $\bm{X}_{A_i}$ and $\bm{X}_{D_i}$ are the approximation and detail coefficient series corresponding to the input time series $\bm{X}_{L}$. $\bm{Y}_{A_i}$ and $\bm{Y}_{D_i}$ are the predicted approximation and detail coefficient series corresponding to the predicted time series $\bm{X}_{T}$. To simplify notation, $\bm{X}_{W_i}$ denotes either $\bm{X}_{A_i}$ or $\bm{X}_{D_i}$. Code is available at https://github.com/Secure-and-Intelligent-Systems-Lab
• Figure 2: WPMixer performance with the varying level of the decomposition $m$.
• Figure 3: Performance of the model with increasing look-back window length $L$.