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

• 成果类型: Article; Early Access
• 署名作者: Kock, Anders B.; Pedersen, Rasmus S.; Sorensen, Jesper R. -V.
• 署名单位: University of Oxford; University of Copenhagen; Danish Finance Institute
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2025.2516190
• 发表日期: 2025
• 关键词: square-root lasso; confidence-intervals; time; models

摘要

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 on unknown population 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 a fully data-driven way. 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.