IndexNet: Timestamp and Variable-Aware Modeling for Time Series Forecasting

TL;DR

IndexNet addresses the neglect of index-related cues in multivariate time series forecasting by introducing an Index Embedding (IE) module that combines Timestamp Embedding (TE) and Channel Embedding (CE) with a lightweight MLP backbone. The TE injects periodic timestamp semantics (minute, hour, day-of-week, etc.), while the CE assigns a trainable identity to each variable, enabling variable-aware dynamics. The model predicts future sequences via an $m$-layer residual MLP, operating on enriched representations $\mathbf{Z}^{tc}$ and yielding $\hat{\mathbf{Y}} \in \mathbb{R}^{N \times T}$, followed by de-normalization. Across 12 real-world datasets, IndexNet achieves competitive or superior performance with strong interpretability and significantly lower computational cost, demonstrating the practical value of explicit index semantics for both long- and short-term forecasting.

Abstract

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.

Figures (5)

• Figure 1: The general timestamp processing strategy in early works and its comparative experimental results with more recent methods. Subfigure (a) illustrates the typical processing of timestamp information before to modeling. Subfigure (b) compares the forecasting performance of different methods with timestamp on the Electricity dataset, with input and output sequence lengths are 96.
• Figure 2: The overall architecture of IndexNet, which consists of three modules: Timestamp Embedding, Channel Embedding, and Forecasting.
• Figure 3: Visualization of Channel Embeddings and multivariate time series from the ETTh1 dataset. (a) shows the 3D projection of learned channel embeddings after dimensionality reduction via PCA. (b), (c), and (d) illustrate the time sequences of selected variable groups.
• Figure 4: Visualization of 24-hour Timestamp Embeddings. Subfigure (a) displays the 3D PCA projection of Timestamp Embeddings on the ETTh1 dataset, while subfigure (b) shows the corresponding visualization on the Weather dataset.
• Figure 5: Visualization of ablation results in Electricity dataset. Subfigure (a) illustrates the difference in capturing week-level periodicity with and without the TE module, while (b) and (c) compare the predictions of two similar channels before and after introducing the CE module.