Stationarity Exploration for Multivariate Time Series Forecasting

TL;DR

This paper introduces APRNet, a novel deep learning model that effectively captures stationary information in multivariate time series by modeling amplitude and phase relationships, improving forecasting accuracy.

Contribution

The paper proposes APRNet, which decouples amplitude and phase modeling and introduces the KLC module for flexible local correlation fitting, advancing multivariate time series forecasting.

Findings

APRNet outperforms state-of-the-art methods in experiments.

Effective modeling of amplitude-phase relationships improves stationary feature extraction.

KLC module enhances local correlation fitting across frequencies.

Abstract

Deep learning-based time series forecasting has found widespread applications. Recently, converting time series data into the frequency domain for forecasting has become popular for accurately exploring periodic patterns. However, existing methods often cannot effectively explore stationary information from complex intertwined frequency components. In this paper, we propose a simple yet effective Amplitude-Phase Reconstruct Network (APRNet) that models the inter-relationships of amplitude and phase, which prevents the amplitude and phase from being constrained by different physical quantities, thereby decoupling the distinct characteristics of signals for capturing stationary information. Specifically, we represent the multivariate time series input across sequence and channel dimensions, highlighting the correlation between amplitude and phase at multiple interaction frequencies. We propose a novel Kolmogorov-Arnold-Network-based Local Correlation (KLC) module to adaptively fit local functions using univariate functions, enabling more flexible characterization of stationary features across different amplitudes and phases. This significantly enhances the model's capability to capture time-varying patterns. Extensive experiments demonstrate the superiority of our APRNet against the state-of-the-arts (SOTAs).