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Oracle inequalities for high dimensional vector autoregressions

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  • Kock, Anders Bredahl
  • Callot, Laurent

Abstract

This paper establishes non-asymptotic oracle inequalities for the prediction error and estimation accuracy of the LASSO in stationary vector autoregressive models. These inequalities are used to establish consistency of the LASSO even when the number of parameters is of a much larger order of magnitude than the sample size. We also state conditions under which no relevant variables are excluded.

Suggested Citation

  • Kock, Anders Bredahl & Callot, Laurent, 2015. "Oracle inequalities for high dimensional vector autoregressions," Journal of Econometrics, Elsevier, vol. 186(2), pages 325-344.
    • Handle: RePEc:eee:econom:v:186:y:2015:i:2:p:325-344
    DOI: 10.1016/j.jeconom.2015.02.013
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    More about this item

    Keywords

    VAR; LASSO; Adaptive LASSO; Oracle inequality; High-dimensional data;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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