Sparse Causal Dynamic Linear Regression

We develop a sparse causal dynamic regression framework for long multivariate time series. With very long time series, the potentially large number of lags and leads in a dynamic regression model often makes time‐domain estimation numerically unstable or intractable. Frequency‐domain estimation offers a stable and computationally efficient alternative, but it tends to generate noncausal, non‐sparse solutions. Noncausality prevents real‐time prediction by relying on future predictor values, and insufficient sparsity hinders interpretability and practical application. Our method applies thresholding operators to the frequency‐domain estimates to obtain causal models that retain only a small, relevant set of variables and lags. The procedure is supported by theory showing that, under mild conditions, it achieves the optimal sparsity rate with only a small increase in mean squared prediction error. A frequency‐domain cross‐validation scheme, with an optional one‐standard‐error rule, selects tuning parameters and promotes parsimony. Simulation studies and a stock index return application demonstrate accurate lag identification, competitive predictive performance, and clear interpretability.