Beiliang Wu

Peiyuan Liu, Beiliang Wu, Naiqi Li et al.

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.

Beiliang Wu, Peiyuan Liu, Yifan Hu et al.

Multivariate time series forecasting (MTSF) plays a vital role in a wide range of real-world applications, such as weather prediction and traffic flow forecasting. Although recent advances have significantly improved the modeling of temporal dynamics and inter-variable dependencies, most existing methods overlook index-related descriptive information, such as timestamps and variable indices, which carry rich contextual semantics. To unlock the potential of such information and take advantage of the lightweight and powerful periodic capture ability of MLP-based architectures, we propose IndexNet, an MLP-based framework augmented with an Index Embedding (IE) module. The IE module consists of two key components: Timestamp Embedding (TE) and Channel Embedding (CE). Specifically, TE transforms timestamps into embedding vectors and injects them into the input sequence, thereby improving the model's ability to capture long-term complex periodic patterns. In parallel, CE assigns each variable a unique and trainable identity embedding based on its index, allowing the model to explicitly distinguish between heterogeneous variables and avoid homogenized predictions when input sequences seem close. Extensive experiments on 12 diverse real-world datasets demonstrate that IndexNet achieves comparable performance across mainstream baselines, validating the effectiveness of our temporally and variably aware design. Moreover, plug-and-play experiments and visualization analyses further reveal that IndexNet exhibits strong generality and interpretability, two aspects that remain underexplored in current MTSF research.