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A restricted eigenvalue condition for unit-root non-stationary data

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  • Etienne Wijler

Abstract

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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  • Etienne Wijler, 2022. "A restricted eigenvalue condition for unit-root non-stationary data," Papers 2208.12990, arXiv.org.
    • Handle: RePEc:arx:papers:2208.12990
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    References listed on IDEAS

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    1. Liao, Zhipeng & Phillips, Peter C. B., 2015. "Automated Estimation Of Vector Error Correction Models," Econometric Theory, Cambridge University Press, vol. 31(3), pages 581-646, June.
    2. Medeiros, Marcelo C. & Mendes, Eduardo F., 2016. "ℓ1-regularization of high-dimensional time-series models with non-Gaussian and heteroskedastic errors," Journal of Econometrics, Elsevier, vol. 191(1), pages 255-271.
    3. Kock, Anders Bredahl & Callot, Laurent, 2015. "Oracle inequalities for high dimensional vector autoregressions," Journal of Econometrics, Elsevier, vol. 186(2), pages 325-344.
    4. Smeekes, Stephan & Wijler, Etienne, 2021. "An automated approach towards sparse single-equation cointegration modelling," Journal of Econometrics, Elsevier, vol. 221(1), pages 247-276.
    5. Koo, Bonsoo & Anderson, Heather M. & Seo, Myung Hwan & Yao, Wenying, 2020. "High-dimensional predictive regression in the presence of cointegration," Journal of Econometrics, Elsevier, vol. 219(2), pages 456-477.
    6. Liang, Chong & Schienle, Melanie, 2019. "Determination of vector error correction models in high dimensions," Journal of Econometrics, Elsevier, vol. 208(2), pages 418-441.
    7. Lee, Ji Hyung & Shi, Zhentao & Gao, Zhan, 2022. "On LASSO for predictive regression," Journal of Econometrics, Elsevier, vol. 229(2), pages 322-349.
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    Cited by:

    1. Alain Hecq & Luca Margaritella & Stephan Smeekes, 2023. "Inference in Non-stationary High-Dimensional VARs," Papers 2302.01434, arXiv.org, revised Sep 2023.
    2. Ziwei Mei & Zhentao Shi, 2022. "On LASSO for High Dimensional Predictive Regression," Papers 2212.07052, arXiv.org, revised Jan 2024.

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