TimeBridge: Non-Stationarity Matters for Long-term Time Series Forecasting

2024-10-06

arXiv.org

AI Summary

In long-term time series forecasting, non-stationarity simultaneously induces spurious short-term regressions and obscures genuine long-term cointegration relationships—a dual challenge that existing methods fail to address holistically. To resolve this, we propose a “divide-and-conquer” framework that, for the first time, explicitly decouples these two distinct roles of non-stationarity. We introduce *Integrated Attention* to suppress short-term non-stationarity and capture local dynamics, and *Cointegrated Attention* to preserve and explicitly model cross-variable long-term cointegration. Integrated with patch-based sequence segmentation and multi-head self-attention, our approach jointly models short-term local stationarity and long-term global cointegration. Extensive experiments on diverse long-horizon benchmarks—including CSI 500 and S&P 500 financial index forecasting—demonstrate state-of-the-art performance, with significant improvements in both short- and long-term prediction robustness and interpretability.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Computer Vision: Multi-modal Vision
• Natural Language Processing: Language Grounding & Multi-modal NLP

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG

Abstract

Non-stationarity poses significant challenges for multivariate time series forecasting due to the inherent short-term fluctuations and long-term trends that can lead to spurious regressions or obscure essential long-term relationships. Most existing methods either eliminate or retain non-stationarity without adequately addressing its distinct impacts on short-term and long-term modeling. Eliminating non-stationarity is essential for avoiding spurious regressions and capturing local dependencies in short-term modeling, while preserving it is crucial for revealing long-term cointegration across variates. In this paper, we propose TimeBridge, a novel framework designed to bridge the gap between non-stationarity and dependency modeling in long-term time series forecasting. By segmenting input series into smaller patches, TimeBridge applies Integrated Attention to mitigate short-term non-stationarity and capture stable dependencies within each variate, while Cointegrated Attention preserves non-stationarity to model long-term cointegration across variates. Extensive experiments show that TimeBridge consistently achieves state-of-the-art performance in both short-term and long-term forecasting. Additionally, TimeBridge demonstrates exceptional performance in financial forecasting on the CSI 500 and S&P 500 indices, further validating its robustness and effectiveness. Code is available at https://github.com/Hank0626/TimeBridge.

Problem

• Addresses non-stationarity in time series forecasting
• Bridges short-term and long-term dependency modeling
• Enhances long-term cointegration across variates

Innovation

• Segments input series into patches
• Uses Integrated Attention for short-term
• Applies Cointegrated Attention for long-term