Abstract:Multivariate time series forecasting faces the fundamental challenge of capturing complex inter-variable dependencies and their dynamic evolution over time. Existing methods often rely on static correlations or black-box attention mechanisms, which struggle to effectively model causal interactions and adapt to non-stationary patterns. To address this issue, this study propose a time series prediction model that integrates causal constraint with dynamic evolution. Specifically, we introduce a causal constraint mechanism that employs constraint-based causal discovery to identify key leading variables, transforms the resulting causal matrix into a graph structure, and applies a graph convolution network (GCN) to aggregate information from causal parent variables into enhanced feature representations. In parallel, we design a dynamic evolution mechanism, which updates both the structure and weights of the causal graph over time to capture non-stationary causal relationships, while jointly optimizing with the forecasting objective to ensure consistency between causal reasoning and predictive performance. The experimental results on eight open multivariate time series benchmark data sets show that the model has improvements on both MSE and MAE, which is superior to the existing strong baseline method. This work not only advances interpretable and adaptive time series forecasting but also provides a novel perspective for causally driven dynamic prediction in complex temporal systems.