Dual-AN: A Hierarchical Framework Synergizes Time and Frequency Domains for Non-stationary Time Series Forecasting

ICLR 2026 Conference Submission15630 Authors

Keywords: Non-stationary Time Series Forecasting, Time and Frequency Domains, Adaptive Normalization

TL;DR: A Hierarchical Framework Synergizes Time and Frequency Domains for Non-stationary Time Series Forecasting

Abstract: To address the pervasive and challenging issue of non-stationarity in time series forecasting, recent research has primarily focused on time-domain normalization methods that separate non-stationary features using statistical indicators. The proposal of frequency adaptive normalization (FAN) offers a new perspective for separating non-stationary components in the frequency domain. However, existing methods remain confined to a single domain, lacking a synergistic integration of time and frequency domains. To bridge this gap, we introduce Dual-AN, a hierarchical framework that synergizes both time and frequency domains. After utilizing the Fourier transform approach to separate non-stationary factors, we propose a novel sliding window adaptive normalization (SWAN) method to eliminate the local non-stationarity in the residuals. Furthermore, we introduce the statistical prediction module (SPM) to forecast future statistics, which are used to de-normalize the outputs based on the statistics of each window. Dual-AN is a general framework that can be easily integrated into any forecasting model. We evaluate the improvement in forecasting performance of 3 different benchmark models on 8 widely-used datasets. The results show that Dual-AN demonstrates significant performance improvement, with the average prediction error MAE and MSE reduced by 15.92% and 20.72%. In comparison with other existing normalization methods, Dual-AN surpasses all existing methods and achieves state-of-the-art (SOTA) performance with an average prediction error reduction of 7.69%.

Primary Area: learning on time series and dynamical systems

Submission Number: 15630