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.

Recent CNN and Transformer-based models tried to utilize frequency and periodicity information for long-term time series forecasting. However, most existing work is based on Fourier transform, which cannot capture fine-grained and local frequency structure. In this paper, we propose a Wavelet-Fourier Transform Network (WFTNet) for long-term time series forecasting. WFTNet utilizes both Fourier and wavelet transforms to extract comprehensive temporal-frequency information from the signal, where Fourier transform captures the global periodic patterns and wavelet transform captures the local ones. Furthermore, we introduce a Periodicity-Weighted Coefficient (PWC) to adaptively balance the importance of global and local frequency patterns. Extensive experiments on various time series datasets show that WFTNet consistently outperforms other state-of-the-art baseline. Code is available at https://github.com/Hank0626/WFTNet.

Convolutional neural network (CNN)-based and Transformer-based methods have recently made significant strides in time series forecasting, which excel at modeling local temporal variations or capturing long-term dependencies. However, real-world time series usually contain intricate temporal patterns, thus making it challenging for existing methods that mainly focus on temporal variations modeling from the 1D time series directly. Based on the intrinsic periodicity of time series, we propose a novel Periodicity Decoupling Framework (PDF) to capture 2D temporal variations of decoupled series for long-term series forecasting. Our PDF mainly consists of three components: multi-periodic decoupling block (MDB), dual variations modeling block (DVMB), and variations aggregation block (VAB). Unlike the previous methods that model 1D temporal variations, our PDF mainly models 2D temporal variations, decoupled from 1D time series by MDB. After that, DVMB attempts to further capture short-term and long-term variations, followed by VAB to make final predictions. Extensive experimental results across seven real-world long-term time series datasets demonstrate the superiority of our method over other state-of-the-art methods, in terms of both forecasting performance and computational efficiency. Code is available at https://github.com/Hank0626/PDF.

Deep neural networks (DNNs) have recently achieved remarkable advancements in time series forecasting (TSF) due to their powerful ability of sequence dependence modeling. To date, existing DNN-based TSF methods still suffer from unreliable predictions for real-world data due to its non-stationarity characteristics, i.e., data distribution varies quickly over time. To mitigate this issue, several normalization methods (e.g., SAN) have recently been specifically designed by normalization in a fixed period/window in the time domain. However, these methods still struggle to capture distribution variations, due to the complex time patterns of time series in the time domain. Based on the fact that wavelet transform can decompose time series into a linear combination of different frequencies, which exhibits distribution variations with time-varying periods, we propose a novel Dual-domain Dynamic Normalization (DDN) to dynamically capture distribution variations in both time and frequency domains. Specifically, our DDN tries to eliminate the non-stationarity of time series via both frequency and time domain normalization in a sliding window way. Besides, our DDN can serve as a plug-in-play module, and thus can be easily incorporated into other forecasting models. Extensive experiments on public benchmark datasets under different forecasting models demonstrate the superiority of our DDN over other normalization methods. Code will be made available following the review process.