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Structural inference in sparse high-dimensional vector autoregressions

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  • Krampe, J.
  • Paparoditis, E.
  • Trenkler, C.

Abstract

We consider statistical inference for impulse responses and forecast error variance decompositions in sparse, structural high-dimensional vector autoregressive (SVAR) systems. We introduce consistent estimators of impulse responses in the high-dimensional setting and suggest valid inference procedures for the same parameters. Statistical inference in our setting is much more involved since standard procedures, like the delta-method, do not apply. By using local projection equations, we first construct a de-sparsified version of regularized estimators of the moving average parameters associated with the VAR system. We then obtain estimators of the structural impulse responses by combining the aforementioned de-sparsified estimators with a non-regularized estimator of the contemporaneous impact matrix, also taking into account the high-dimensionality of the system. We show that the distribution of the derived estimators of structural impulse responses has a Gaussian limit. We also present a valid bootstrap procedure to estimate this distribution. Applications of the inference procedure in the construction of confidence intervals for impulse responses as well as in tests for forecast error variance decomposition are presented. Our procedure is illustrated by means of simulations and an empirical application.

Suggested Citation

  • Krampe, J. & Paparoditis, E. & Trenkler, C., 2023. "Structural inference in sparse high-dimensional vector autoregressions," Journal of Econometrics, Elsevier, vol. 234(1), pages 276-300.
  • Handle: RePEc:eee:econom:v:234:y:2023:i:1:p:276-300
    DOI: 10.1016/j.jeconom.2022.01.003
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    4. Jonas Krampe & Luca Margaritella, 2024. "Global bank network connectedness revisited: What is common, idiosyncratic and when?," Papers 2402.02482, arXiv.org.
    5. Endong Wang, 2024. "Structural counterfactual analysis in macroeconomics: theory and inference," Papers 2409.09577, arXiv.org.

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