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...

We focus on the high dimensional linear regression Y∼N(Xβ∗,σ2In), where β∗∈Rp is the parameter of interest. In this setting, several estimators such as the LASSO (Tibshirani, 1996) and the Dantzig Selector (Candes and Tao, 2007) are known to satisfy interesting properties whenever the...