Title: DeFa: Non-Stationary Decomposition and Factorized Forecasting for Multivariate Time Series
Primary area: learning on time series and dynamical systems
Keywords: time series forecasting, deep learning

Abstract: Multivariate time series forecasting is essential in fields like energy systems, weather prediction, and traffic monitoring. While recent deep learning models, including Transformer-based architectures, show potential, they often struggle to capture the complex dynamics and non-stationary patterns inherent in real-world data. This limitation arises from over-parametrization and the difficulty in modelling shifting patterns in simple short- and long-term terms. In this paper, we propose a unified framework, DeFa, that addresses these challenges by combining decomposition-based modelling with tensor autoregressive forecasting. To capture long-term dynamics, stationary seasonality, and sparse residuals unique to non-stationary time series, DeFa decomposes the input series into three components using the Non-stationary AdaptiveInteractive Long-term strategy (NAILong). Furthermore, to improve the prediction of the Amplifier, which encodes time-varying dynamics, DeFa is enhanced with the Factorized Tensor Autoregression framework (FaTA). Unlike existing methods that disentangle or represent input series directly, FaTA explicitly models the autoregressive coefficient tensor across variates and temporal dimensions. This fusion enables a more flexible and interpretable representation of multi-variable interactions, improving forecasting accuracy while maintaining computational efficiency. Extensive experiments on real-world datasets show that DeFa outperforms state-of-the-art methods in terms of both interpretable forecasting accuracy and scalability. Additionally, DeFa handles long-term dynamics and drifting seasonalities efficiently through a plug-in option, extending its adaptability.

TL;DR: DeFA introduces a decomposition-based framework with tensor autoregressive forecasting that effectively captures non-stationary dynamics and long-term dependencies in multivariate time series.