WaveletMixer: A Multi-Resolution Wavelets Based MLP-Mixer for Multivariate Long-Term Time Series Forecasting

Time Series Forecasting (TSF) aims at predicting future values for a time series data and plays a crucial role in many real-world applications, e.g., finance, disease spread, or weather predictions. However, it is also a very challenging task due to complex temporal dependencies in the data, especially for long-term forecasting. In this paper, we introduce WaveletMixer, an iterative multi-levels, multi-resolutions and multi-phases approach to effectively capture long-term dependencies of multivariate time series in both global and local perspectives for improving forecasting performance. WaveletMixer fundamentally differs from existing works in the following key aspects. First, it exploits multi-levels properties of Wavelet transformation to create multiple forecasting models for different frequency domains at various levels of resolutions. Second, the relationships among different frequency domains are exploited to iteratively adjust all prediction models at all levels simultaneously in both local and global perspectives to reduce prediction errors and biases, thus significantly improving the final accuracy. Third, while WaveletMixer is a general framework that can be used to boost the performance of any deep-learning architecture (e.g., MLP, LSTM or Transformer), we additionally introduce TS-Learner, an MLP-based model to further enhance the performance in long-term forecasting. Extensive experiments have been conducted on nine real-world datasets to demonstrate the outstanding performance of WaveletMixer compared to SOTA methods and to reveal its important characteristics.