PMDformer: Patch-Mean Decoupling Information Transformer for Long-term Forecasting

Long-term time series forecasting (LTSF) plays a crucial role in fields such as energy management, finance, and traffic prediction. Transformer-based models have adopted patch-based strategies to capture long-range dependencies, but accurately modeling shape similarities across patches and variables remains challenging due to scale differences. To address this, we introduce patch-mean decoupling (PMD), which separates the trend and residual shape information by subtracting the mean of each patch, preserving the original structure and ensuring that the attention mechanism captures true shape similarities. Futhermore, to more effectively model long-range dependencies and capture cross-variable relationships, we propose Trend Restoration Attention (TRA) and Proximal Variable Attention (PVA). The former module reintegrates the decoupled trend from PMD while calculating attention output. And the latter focuses cross-variable attention on the most relevant, recent time segments to avoid overfitting on outdated correlations. Combining these components, we propose PMDformer, a model designed to effectively capture shape similarity in long-term forecasting scenarios. Extensive experiments indicate that PMDformer outperforms existing state-of-the-art methods in stability and accuracy across multiple LTSF benchmarks. The code is available at https://github.com/aohu1105/PMDformer.

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

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