Oracle inequalities for high dimensional vector autoregressions

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 magnit...

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Bibliographic Details
Published in:Journal of econometrics 2015-06, Vol.186 (2), p.325-344
Main Authors: Kock, Anders Bredahl, Callot, Laurent
Format: Article
Language:English
Subjects:
Adaptive LASSO
Asymptotic methods
Coefficients
Convergence
Econometrics
Economic theory
Estimating techniques
Estimation
High-dimensional data
Inequality
LASSO
Oracle inequality
Probability
Regression analysis
Sparsity
Studies
VAR
Vector-autoregressive models
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Summary: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. Next, non-asymptotic probabilities are given for the adaptive LASSO to select the correct sparsity pattern. We then provide conditions under which the adaptive LASSO reveals the correct sparsity pattern asymptotically. We establish that the estimates of the non-zero coefficients are asymptotically equivalent to the oracle assisted least squares estimator. This is used to show that the rate of convergence of the estimates of the non-zero coefficients is identical to the one of least squares only including the relevant covariates.
ISSN:0304-4076
1872-6895
DOI:10.1016/j.jeconom.2015.02.013