Anders Bredahl Kock, Rasmus Søndergaard Pedersen, Jesper Riis-Vestergaard Sørensen
arXiv 11 Mar 2024 · Econometrics · publishedJournal of the American Statistical Association (2025) · 20 citations (OpenAlex)
arXiv:2403.06657 · PDF · DOI · OpenAlex · Extracted main text
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, e.g., 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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Kock, A. B. and Callot, L (2015) Oracle inequalities for high dimensional vector autoregressions self | 1.000 | 10 | 3 | 100% |
| 2 | Wong, K. C., Li, Z., and Tewari, A (2020) Lasso guarantees for $$-mixing heavy-tailed time series | 1.000 | 8 | 3 | 100% |
| 3 | Belloni, A., Chernozhukov, V., and Wang, L (2011) Square-root lasso: pivotal recovery of sparse signals via conic programming | 0.928 | 5 | 3 | 80% |
| 4 | Masini, R. P., Medeiros, M. C., and Mendes, E. F (2022) Regularized estimation of high-dimensional vector autoregressions with weakly dependent innovations | 0.874 | 8 | 2 | 100% |
| 5 | Miao, L., Phillips, P. C. B., and Su, L (2023) High-dimensional vars with common factors | 0.874 | 8 | 2 | 100% |
| 6 | Basu, S. and Michailidis, G (2015) Regularized estimation in sparse high-dimensional time series models | 0.811 | 4 | 2 | 100% |
| 7 | Gao, L., Shao, Q.-M., and Shi, J (2022) Refined Cramér-type moderate deviation theorems for general self-normalized sums with applications to dependent random variables… | 0.794 | 6 | 4 | 50% |
| 8 | Belloni, A., Chen, D., Chernozhukov, V., and Hansen, C (2012) Sparse models and methods for optimal instruments with an application to eminent domain | 0.773 | 13 | 6 | 46% |
| 9 | Medeiros, M. C. and Mendes, E. F (2016) $_1$-regularization of high-dimensional time-series models with non-gaussian and heteroskedastic errors | 0.737 | 3 | 2 | 100% |
| 10 | Adamek, R., Smeekes, S., and Wilms, I (2023) Lasso inference for high-dimensional time series | 0.737 | 3 | 2 | 100% |
Showing the top 10 of 40 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Sparse High-Dimensional Vector Autoregressive Bootstrap | 0.843 | 3 | 3 |
| 2 | Tuning Parameter Selection in Econometrics | 0.511 | 2 | 1 |
| 3 | Sparse Tree-Based Aggregation for Time Series Regressions | 0.405 | 1 | 1 |