TwinS: Revisiting Non-Stationarity in Multivariate Time Series Forecasting

Multivariate time series forecasting (MTSF) has gained widespread prominence in real-world applications, such as weather prediction, financial risk assessment, and traffic forecasting. Transformers (Vaswani et al., 2017) have emerged as the most popular approach for this task, primarily attributed to their power in capturing temporal dependencies Wen et al. (2023). Recent advances (Wu et al., 2021; Liu et al., 2021a; Zhou et al., 2022; Nie et al., 2023) have further bolstered the popularity. A long-lasting challenge in the realm of MTSF lies in effectively mitigating the non-stationarity inherent in real-world time series. In general, non-stationary time series exhibits a persistent alteration in its statistical attributes (e.g., mean and variance) and joint distribution across time, thereby diminishing its predictability. In previous work, several models have utilized time series pre-processing techniques (Passalis et al., 2019; Kim et al., 2021) to achieve stationarity or involved statistical guidance during model training (Liu et al., 2022b), resulting in significant performance enhancements. Though promising, the above endeavors still fall short of modeling the non-stationary period distribution. To verify this point, we empirically leverage the Morlet wavelet transform on the Weather dataset (Wu et al., 2021), leading to the energy distribution in Fig 1. We observe that (i) Non-stationary time series comprises multiple nested and overlapping periods, with diverse periodic patterns and varying strengths at each time step.