TimeCNN: Refining Cross-Variable Interaction on Time Point for Time Series Forecasting

TL;DR

Given historical multivariate time series $ extbf{X} \in \mathbb{R}^{L\times N}$, the task is to forecast $ extbf{Y} \in \mathbb{R}^{T\times N}$, where cross-variable correlations are multifaceted and evolve over time. TimeCNN introduces a timepoint-independent CrossCNN that assigns an independent convolution kernel to each time point, enabling explicit modeling of dynamic, including negative, correlations among variables. Empirical results across 12 real-world datasets show TimeCNN achieves state-of-the-art accuracy while drastically reducing computational cost (e.g., MACs down by about 60%, parameters down by about 57%) and accelerating inference by 3–4× compared with iTransformer and other baselines. The approach demonstrates robust performance and efficiency, with strong ablations and robustness analyses suggesting practical applicability and potential for further extensions in scalable, dynamic cross-variable modeling.

Abstract

Time series forecasting is extensively applied across diverse domains. Transformer-based models demonstrate significant potential in modeling cross-time and cross-variable interaction. However, we notice that the cross-variable correlation of multivariate time series demonstrates multifaceted (positive and negative correlations) and dynamic progression over time, which is not well captured by existing Transformer-based models. To address this issue, we propose a TimeCNN model to refine cross-variable interactions to enhance time series forecasting. Its key innovation is timepoint-independent, where each time point has an independent convolution kernel, allowing each time point to have its independent model to capture relationships among variables. This approach effectively handles both positive and negative correlations and adapts to the evolving nature of variable relationships over time. Extensive experiments conducted on 12 real-world datasets demonstrate that TimeCNN consistently outperforms state-of-the-art models. Notably, our model achieves significant reductions in computational requirements (approximately 60.46%) and parameter count (about 57.50%), while delivering inference speeds 3 to 4 times faster than the benchmark iTransformer model

Figures (11)

• Figure 1: A case visualization of variable relationships dynamically changing over time. Pearson correlation coefficients are calculated for each of four equal consecutive segments of the lookback window, using 50 randomly selected variables from the Traffic dataset.
• Figure 2: Comparison of two univariable time series from the ECL dataset, with the x-axis representing the lookback window and the y-axis showing variable values at each time step. Purple and red dashed boxes indicate positive and negative correlations.
• Figure 3: Comparison between the Transformer Transformer, iTransformer itransformer, and TimeCNN. The Transformer embeds all variables at each time point into temporal tokens, using attention to capture cross-time interactions. The iTransformer embeds time points of each variable into variable tokens, leveraging attention for cross-variable interactions. In contrast, our proposed TimeCNN processes each time point independently to capture and model dynamic changes in variable relationships.
• Figure 4: Performance of TimeCNN. The results of PatchTST PatchTST and TimeCNN are from our experiments and other average results (MSE) are reported following iTransformer itransformer.
• Figure 5: The TimeCNN architecture, which mainly consists of CrossCNN, Embedding, Feed-Forward Networks (FFN), and Projection for prediction. In the CrossCNN module, cross-variable interactions at each time point are captured. Then, the entire time series of each variable is embedded into variable tokens, which are further learned in shared FFN. Finally, the learned multivariate representations are projected through a linear layer to predict future time series.