Multi-period Normalization for Long-term Time Series Forecasting

Recent advancements in deep learning have significantly improved multivariate time series forecasting by leveraging powerful modeling techniques. However, the non-stationary nature of time series data, where distributions shift rapidly over time, continues to challenge the effectiveness of existing methods. In this paper, we propose a novel Multi-period Normalization, dubbed MPNorm, to address these complex distributional changes across multiple periods dynamically. MPNorm first analyzes periodic patterns of the training set to identify stable periods. Then, it filters subsequences for each period via frequency domain operations and normalizes them in the Multi-period Normalization Block, generating stable subsequences and distribution characteristics. These stable subsequences are weighted according to the amplitude intensity of each period. Besides, MPNorm employs residual learning to predict distributional characteristics of future series. Extensive experiments show that MPNorm significantly enhances mainstream long-term time series forecasting models and achieves state-of-the-art performance compared to representative normalization methods.