FredNormer: Frequency Domain Normalization for Non-stationary Time Series Forecasting

Recent normalization-based methods have shown great success in tackling the distribution shift issue, facilitating non-stationary time series forecasting. Since these methods operate in the time domain, they may fail to fully capture the dynamic patterns that are more apparent in the frequency domain, leading to suboptimal results. This paper first theoretically analyzes how normalization methods affect frequency components. We prove that the current normalization methods that operate in the time domain uniformly scale non-zero frequencies, and thus, they struggle to determine components that contribute to more robust forecasting. Therefore, we propose FredNormer, which observes datasets from a frequency perspective and adaptively up-weights the key frequency components. To this end, FredNormer consists of two components: a statistical metric that normalizes the input samples based on their frequency stability and a learnable weighting layer that adjusts stability and introduces sample-specific variations. Notably, FredNormer is a plug-and-play module, which does not compromise the efficiency compared to existing normalization methods. Extensive experiments show that FredNormer improves the averaged MSE of backbone forecasting models by 33.3% and 55.3% on the ETTm2 dataset. Compared to the baseline normalization methods, FredNormer achieves 18 top-1 results and 6 top-2 results out of 28 settings.