A causal delay-embedding spatiotemporal framework for multivariate time series forecasting

Recent advancements in deep neural networks have markedly enhanced multivariate time series forecasting. However, data-driven forecasting of high-dimensional nonlinear dynamical systems remains a pivotal challenge. Accurate forecasting and feature extraction are often hindered by environmental noise and complex spatiotemporal couplings, where traditional embedding strategies fail to distinguish genuine causal drivers from spurious correlations. To address this, we propose the Temporal Convolutional and Causal Delay-Embedding-based Forecast Machine (TC-DEFM). By internalizing a causally-inspired dynamic intervention proxy as a structural inductive bias, this framework effectively bridges the gap between causal inference and deep representation learning. Specifically, we design a Temporal Causal Layer (TCL) that dynamically purifies the input space via difference intervention effects and sparsity constraints. Furthermore, a Hybrid Spatiotemporal Encoder is constructed by integrating causal convolutions (TCN) with the Transformer architecture to capture both local transients and global evolutionary trends. Extensive experiments on the Lorenz-96 chaotic system and real-world datasets demonstrate that TC-DEFM achieves superior prediction accuracy and exhibits substantial improvements in long-term forecasting stability and robustness against noise. The results validate the framework's capability in effectively learning robust representations and serving as a highly effective neural architecture for analyzing complex spatiotemporal dynamics.