Regularized Estimation of High-Dimensional Vector AutoRegressions with Weakly Dependent Innovations

Abstract

There has been considerable advance in understanding the properties of sparse regularization procedures in high-dimensional models. In time series context, it is mostly restricted to Gaussian autoregressions or mixing sequences. We study oracle properties of LASSO estimation of weakly sparse vector-autoregressive models with heavy tailed, weakly dependent innovations with virtually no assumption on the conditional heteroskedasticity. In contrast to current literature, our innovation process satisfy an L^1 mixingale type condition on the centered conditional covariance matrices. This condition covers L^1-NED sequences and strong (-) mixing sequences as particular examples.

Tasks

Reproductions