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

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.

Forecasting things like stock trends or weather patterns can be tricky, especially when the data we use keeps changing over time. These changes — known as non-stationarity — include short-term ups and downs as well as long-term trends, and both can confuse traditional forecasting methods.Our new method, called TimeBridge, is designed to deal with this challenge in a smarter way. Instead of treating all changes the same, it looks at short-term and long-term patterns separately. For the short term, it cleans out the noise to focus on recent, reliable patterns. For the long term, it keeps important trends so the model can understand deeper relationships across different types of data.In tests, TimeBridge consistently made more accurate predictions than existing tools. It also did especially well on real-world financial data like the CSI 500 and S&P 500 stock indices, showing its strength in both research and practical use.