Stationarity Exploration for Multivariate Time Series Forecasting

2025-08-12

AI Summary

To address the challenges of entangled frequency-domain components and ineffective extraction of stationarity information in multivariate time series forecasting, this paper proposes the Amplitude-Phase Reconstruction Network (APRNet). Methodologically, APRNet jointly models the dynamic interactions between amplitude and phase to decouple signal features and explicitly capture stationary patterns. It further introduces a Kolmogorov–Arnold-based Local Correlation module (KLC) that adaptively fits local nonlinear functions of amplitude-phase combinations across multiple frequencies, enhancing flexibility in representing stationary features. By integrating frequency-domain transformation with dual-dimensional modeling—along both temporal and channel axes—APRNet achieves significant improvements over state-of-the-art methods on multiple benchmark datasets. Experimental results validate its superior capability in modeling time-varying stationary structures and its effectiveness in boosting forecasting accuracy.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Planning, Routing, and Scheduling: Activity and Plan Recognition
• Computer Vision: Multi-modal Vision

Application Category

• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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).

Problem

• Exploring stationary information in complex frequency components
• Decoupling amplitude and phase for better signal characterization
• Adaptively capturing time-varying patterns in multivariate time series

Innovation

• Amplitude-Phase Reconstruct Network for decoupling signals
• Kolmogorov-Arnold-Network-based Local Correlation module
• Multivariate time series representation across dimensions