Title: Hierarchical Periodic Stationarization for Non-stationary Time Series Forecasting
Primary area: learning on time series and dynamical systems
Keywords: Time series, Stationarization, Non-stationarity, Forecasting, Long-range dependency

Abstract: Time series forecasting (TSF) has advanced rapidly through benchmark-driven competition. However, we find that state-of-the-art models struggle to predict even a simple long-period sine wave, despite ample training data. One reason is that existing benchmarks underrepresent the non-stationary characteristics prevalent in real-world time series, leading to misleading evaluations. Moreover, standard stationarization methods inherently introduce substantial information loss during the stationarization process. To investigate this, we introduce \textit{controlled} datasets that expose information loss incurred by standard z-normalization-based stationarization methods, widely used in TSF models. To address this limitation, we propose Hipeen, a hierarchical periodic stationarization method that achieves stationarization through representing the value into multiple periodic components, minimizing information loss. Hipeen, with a linear backbone, successfully forecasts highly non-stationary signals—controlled datasets and large-scale stock datasets—substantially outperforming current SOTA models (6 stationarization methods and 8 baselines), while maintaining strong performance on conventional benchmarks. Our results highlight the importance of preserving critical information during stationarization and provide a new approach for robust TSF in non-stationary environments. All code and models will be released in the final version.

TL;DR: Demonstrating that time series forecasting models employing normalization-based stationarization (ReVIN) face fundamental limitations on non-stationary data, a novel stationarization method is proposed to overcome them.