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Sparse Causal Dynamic Linear Regression
Journal article   Open access   Peer reviewed

Sparse Causal Dynamic Linear Regression

Rui Huang and Kung-Sik Chan
Journal of time series analysis
06/07/2026
DOI: 10.1111/jtsa.70068
Appears in  UI Libraries Support Open Access
url
https://doi.org/10.1111/jtsa.70068View
Published (Version of record) Open Access

Abstract

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.
 causality dynamic linear regression frequency-domain estimation lag selection soft-thresholding sparsity UIOWA OA Agreement

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