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Oracle Inequalities for High Dimensional Vector Autoregressions

Anders Kock and Laurent Callot ()

CREATES Research Papers from Department of Economics and Business Economics, Aarhus University

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.

Keywords: Vector autoregression; LASSO; Adaptive LASSO; Oracle inequality; Variable selection. (search for similar items in EconPapers)
JEL-codes: C01 C02 C13 C32 (search for similar items in EconPapers)
Pages: 22
Date: 2012
New Economics Papers: this item is included in nep-ecm and nep-ets
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Journal Article: Oracle inequalities for high dimensional vector autoregressions (2015) Downloads
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