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Oracle Inequalities for High Dimensional Vector Autoregressions

Author

Listed:
  • Anders Bredahl Kock

    (Aarhus University and CREATES)

  • Laurent A.F. Callot

    (Aarhus University and CREATES)

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. Furthermore, it is shown that under suitable conditions the number of variables selected is of the right order of magnitude and that no relevant variables are excluded. Next, non-asymptotic probabilities are given for the Adaptive LASSO to select the correct sign pattern (and hence the correct sparsity pattern). Finally conditions under which the Adaptive LASSO reveals the correct sign pattern with probability tending to one are given. Again, the number of parameters may be much larger than the sample size. Some maximal inequalities for vector autoregressions which might be of independent interest are contained in the appendix.

Suggested Citation

  • Anders Bredahl Kock & Laurent A.F. Callot, 2012. "Oracle Inequalities for High Dimensional Vector Autoregressions," CREATES Research Papers 2012-16, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2012-16
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Vector autoregression; LASSO; Adaptive LASSO; Oracle inequality; Variable selection.;
    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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