IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2208.12990.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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.

Suggested Citation

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

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2208.12990
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ziwei Mei & Zhentao Shi, 2022. "On LASSO for High Dimensional Predictive Regression," Papers 2212.07052, arXiv.org, revised Jan 2024.
    2. Fan, Rui & Lee, Ji Hyung & Shin, Youngki, 2023. "Predictive quantile regression with mixed roots and increasing dimensions: The ALQR approach," Journal of Econometrics, Elsevier, vol. 237(2).
    3. Lee, Ji Hyung & Shi, Zhentao & Gao, Zhan, 2022. "On LASSO for predictive regression," Journal of Econometrics, Elsevier, vol. 229(2), pages 322-349.
    4. Ricardo P. Masini & Marcelo C. Medeiros & Eduardo F. Mendes, 2023. "Machine learning advances for time series forecasting," Journal of Economic Surveys, Wiley Blackwell, vol. 37(1), pages 76-111, February.
    5. Smeekes, Stephan & Wijler, Etienne, 2018. "Macroeconomic forecasting using penalized regression methods," International Journal of Forecasting, Elsevier, vol. 34(3), pages 408-430.
    6. Smeekes, Stephan & Wijler, Etienne, 2021. "An automated approach towards sparse single-equation cointegration modelling," Journal of Econometrics, Elsevier, vol. 221(1), pages 247-276.
    7. Andrii Babii & Eric Ghysels & Jonas Striaukas, 2024. "High-Dimensional Granger Causality Tests with an Application to VIX and News," Journal of Financial Econometrics, Oxford University Press, vol. 22(3), pages 605-635.
    8. Christian Brownlees & Gu{dh}mundur Stef'an Gu{dh}mundsson, 2021. "Performance of Empirical Risk Minimization for Linear Regression with Dependent Data," Papers 2104.12127, arXiv.org, revised May 2023.
    9. David Neto, 2023. "Penalized leads-and-lags cointegrating regression: a simulation study and two empirical applications," Empirical Economics, Springer, vol. 65(2), pages 949-971, August.
    10. Jonas Krampe & Luca Margaritella, 2021. "Factor Models with Sparse VAR Idiosyncratic Components," Papers 2112.07149, arXiv.org, revised May 2022.
    11. 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.
    12. Chaohua Dong & Jiti Gao & Bin Peng & Yundong Tu, 2021. "Multiple-index Nonstationary Time Series Models: Robust Estimation Theory and Practice," Papers 2111.02023, arXiv.org.
    13. Yousuf, Kashif & Ng, Serena, 2021. "Boosting high dimensional predictive regressions with time varying parameters," Journal of Econometrics, Elsevier, vol. 224(1), pages 60-87.
    14. Andrii Babii & Eric Ghysels & Jonas Striaukas, 2022. "Machine Learning Time Series Regressions With an Application to Nowcasting," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(3), pages 1094-1106, June.
    15. Matteo Barigozzi & Christian Brownlees, 2019. "NETS: Network estimation for time series," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(3), pages 347-364, April.
    16. Adamek, Robert & Smeekes, Stephan & Wilms, Ines, 2023. "Lasso inference for high-dimensional time series," Journal of Econometrics, Elsevier, vol. 235(2), pages 1114-1143.
    17. Liang, Chong & Schienle, Melanie, 2019. "Determination of vector error correction models in high dimensions," Journal of Econometrics, Elsevier, vol. 208(2), pages 418-441.
    18. Thilo Reinschlussel & Martin C. Arnold, 2024. "Information-Enriched Selection of Stationary and Non-Stationary Autoregressions using the Adaptive Lasso," Papers 2402.16580, arXiv.org, revised Jul 2024.
    19. Zhou, Weilun & Gao, Jiti & Harris, David & Kew, Hsein, 2024. "Semi-parametric single-index predictive regression models with cointegrated regressors," Journal of Econometrics, Elsevier, vol. 238(1).
    20. Chaohua Dong & Jiti Gao & Bin Peng & Yundong Tu, 2023. "Robust M-Estimation for Additive Single-Index Cointegrating Time Series Models," Monash Econometrics and Business Statistics Working Papers 2/23, Monash University, Department of Econometrics and Business Statistics.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2208.12990. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.