arXiv 27 Aug 2022 · Econometrics · 1 citations (OpenAlex)
arXiv:2208.12990 · PDF · DOI · OpenAlex · Extracted main text
In this paper, we develop a restricted eigenvalue condition for unit-root non-stationary data and derive its validity under the assumption of independent Gaussian innovations that may be contemporaneously correlated. The method of proof relies on matrix concentration inequalities and offers sufficient flexibility to enable extensions of our results to alternative time series settings. As an application of this result, we show the consistency of the lasso estimator on ultra high-dimensional cointegrated data in which the number of integrated regressors may grow exponentially in relation to the sample size.
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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 | 0.511 | 3 | 2 | 33% |
| 2 | Bickel, P. J., Ritov, Y., and Tsybakov, A. B (2009) Simultaneous analysis of lasso and dantzig selector | 0.511 | 2 | 2 | 50% |
| 3 | Basu, S. and Michailidis, G (2015) Regularized estimation in sparse high-dimensional time series models | 0.511 | 2 | 1 | 100% |
| 4 | Masini, R. P., Medeiros, M. C., and Mendes, E. F (2019) Regularized estimation of high-dimensional vector autoregressions with weakly dependent innovations | 0.511 | 2 | 1 | 100% |
| 5 | Medeiros, M. C. and Mendes, E. F (2016) $_1$-regularization of high-dimensional time series models with non-gaussian and heteroskedastic errors | 0.511 | 2 | 1 | 100% |
| 6 | Smeekes, S. and Wijler, E (2020) An automated approach towards sparse single-equation cointegration modelling self | 0.511 | 2 | 1 | 100% |
| 7 | Kasiviswanathan, S. P. and Rudelson, M (2018) Restricted eigenvalue from stable rank with applications to sparse linear regression | 0.405 | 1 | 1 | 100% |
| 8 | Koo, B., Anderson, H. M., Seo, M. H., and Yao, W (2020) High-dimensional predictive regression in the presence of cointegration | 0.405 | 1 | 1 | 100% |
| 9 | Lee, J. H., Shi, Z., and Gao, Z (2021) On lasso for predictive regression | 0.405 | 1 | 1 | 100% |
| 10 | Liang, C. and Schienle, M (2019) Determination of vector error correction models in high dimensions | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 20 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | On LASSO for High Dimensional Predictive Regression | 0.874 | 7 | 2 |
| 2 | Inference in Non-stationary High-Dimensional VARs | 0.585 | 3 | 1 |