Data-Driven Tuning Parameter Selection for High-Dimensional Vector Autoregressions

Anders Kock

doi:10.1080/01621459.2025.2516190

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Data-Driven Tuning Parameter Selection for High-Dimensional Vector Autoregressions

2025-08-08

Anders Kock

Rasmus S. Pedersen

Jesper Sørensen *

DOI：10.1080/01621459.2025.2516190

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Abstract

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Lasso-type estimators are routinely used to estimate high-dimensional time series models. The theoretical guarantees established for these estimators typically require the penalty level to be chosen in a suitable fashion often depending onunknownpopulation quantities. Furthermore, the resulting estimates and the number of variables retained in the model depend crucially on the chosen penalty level. However, there is currently no theoretically founded guidance for this choice in the context of high-dimensional time series. Instead, one resorts to selecting the penalty level in an ad hoc manner using, for example, information criteria or cross-validation. We resolve this problem by considering estimation of the perhaps most commonly employed multivariate time series model, the linear vector autoregressive (VAR) model, and propose versions of the Lasso, post-Lasso, and square-root Lasso estimators with penalization chosen in afully data-drivenway. The theoretical guarantees that we establish for the resulting estimation and prediction errors match those currently available for methods based on infeasible choices of penalization. We thus provide a first solution for choosing the penalization in high-dimensional time series models. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Keywords:

l1 -penalized estimation

Data-driven tuning parameter selection

High-dimensional time series

Vector autoregressive model