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Sparse High-Dimensional Vector Autoregressive Bootstrap

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  • Robert Adamek
  • Stephan Smeekes
  • Ines Wilms

Abstract

We introduce a high-dimensional multiplier bootstrap for time series data based capturing dependence through a sparsely estimated vector autoregressive model. We prove its consistency for inference on high-dimensional means under two different moment assumptions on the errors, namely sub-gaussian moments and a finite number of absolute moments. In establishing these results, we derive a Gaussian approximation for the maximum mean of a linear process, which may be of independent interest.

Suggested Citation

  • Robert Adamek & Stephan Smeekes & Ines Wilms, 2023. "Sparse High-Dimensional Vector Autoregressive Bootstrap," Papers 2302.01233, arXiv.org.
    • Handle: RePEc:arx:papers:2302.01233
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    File URL: http://arxiv.org/pdf/2302.01233
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    References listed on IDEAS

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    1. Ricardo P. Masini & Marcelo C. Medeiros & Eduardo F. Mendes, 2022. "Regularized estimation of high‐dimensional vector autoregressions with weakly dependent innovations," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(4), pages 532-557, July.
    2. Joseph P. Romano & Michael Wolf, 2005. "Exact and Approximate Stepdown Methods for Multiple Hypothesis Testing," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 94-108, March.
    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. 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.
    5. Yoosoon Chang & Joon Y. Park, 2003. "A Sieve Bootstrap For The Test Of A Unit Root," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(4), pages 379-400, July.
    6. Adamek, Robert & Smeekes, Stephan & Wilms, Ines, 2023. "Lasso inference for high-dimensional time series," Journal of Econometrics, Elsevier, vol. 235(2), pages 1114-1143.
    7. Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2012. "Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors," Papers 1212.6906, arXiv.org, revised Jan 2018.
    8. Kilian,Lutz & Lütkepohl,Helmut, 2018. "Structural Vector Autoregressive Analysis," Cambridge Books, Cambridge University Press, number 9781107196575, October.
    9. Park, Joon Y., 2002. "An Invariance Principle For Sieve Bootstrap In Time Series," Econometric Theory, Cambridge University Press, vol. 18(2), pages 469-490, April.
    10. Trapani, Lorenzo, 2013. "On bootstrapping panel factor series," Journal of Econometrics, Elsevier, vol. 172(1), pages 127-141.
    11. Paparoditis, Efstathios, 1996. "Bootstrapping Autoregressive and Moving Average Parameter Estimates of Infinite Order Vector Autoregressive Processes," Journal of Multivariate Analysis, Elsevier, vol. 57(2), pages 277-296, May.
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