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Estimation of High Dimensional Vector Autoregression via Sparse Precision Matrix

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  • Benjamin Poignard

    (Graduate School of Economics, Osaka University)

  • Manabu Asai

    (Faculty of Economics, Soka University)

Abstract

We consider the problem of estimating sparse structural vector autoregression (SVAR) processes via penalized precision matrix. Such matrix is the output of the underlying directed acyclic graph of the SVAR process, whose zero components correspond to zero SVAR coecients. The precision matrix estimators are deduced from the class of Bregman divergences and regularized by the SCAD, MCP and LASSO penalties. Under suitable regularity conditions, we derive error bounds for the regularized precision matrix for each Bregman divergence. Moreover, we establish the support recovery property, including the case when the penalty is non-convex. These theoretical results are supported by empirical studies.

Suggested Citation

  • Benjamin Poignard & Manabu Asai, 2021. "Estimation of High Dimensional Vector Autoregression via Sparse Precision Matrix," Discussion Papers in Economics and Business 21-03, Osaka University, Graduate School of Economics.
    • Handle: RePEc:osk:wpaper:2103
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    References listed on IDEAS

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    Cited by:

    1. Christis Katsouris, 2023. "High Dimensional Time Series Regression Models: Applications to Statistical Learning Methods," Papers 2308.16192, arXiv.org.

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    Keywords

    sparse structural vector autoregression; statistical consistency; support recovery.;
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