Nonstationary Time Series Forecasting via Unknown Distribution Adaptation

Abstract

As environments evolve, temporal distribution shifts can degrade time series forecasting performance. A straightforward solution is to adapt to nonstationary changes while preserving stationary dependencies. Hence, some methods disentangle stationary and nonstationary components by assuming uniform distribution shifts, but it is impractical since when the distribution changes is unknown. To address this challenge, we propose the \textbf{U}nknown \textbf{D}istribution \textbf{A}daptation (\textbf{UDA}) model for nonstationary time series forecasting, which detects when distribution shifts occur and disentangles stationary/nonstationary latent variables, thus enabling adaptation to unknown distribution without assuming a uniform distribution shift. Specifically, under a Hidden Markov assumption of latent environments, we demonstrate that the latent environments are identifiable. Sequentially, we further disentangle stationary/nonstationary latent variables by leveraging the variability of historical information. Based on these theoretical results, we propose a variational autoencoder-based model, which incorporates an autoregressive hidden Markov model to estimate latent environments. Additionally, we further devise the modular prior networks to disentangle stationary/nonstationary latent variables. These two modules realize automatic adaptation and enhance nonstationary forecasting performance. Experimental results on several datasets validate the effectiveness of our approach.