  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 give 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 give 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.
