This chapter covers penalized regression in the framework of linear time series models and reviews the most commonly used penalized estimators in applied work, namely Ridge Regression, the Least Absolute Shrinkage and Selection Operator (Lasso), the Elastic Net, the adaptive versions of the...

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...