Estimation of high-dimensional vector autoregression via sparse precision matrix

Abstract

Summary We consider the problem of estimating sparse vector autoregression (VAR) via penalized precision matrices. This matrix is the output of the underlying directed acyclic graph of the VAR process, whose zero components correspond to the zero coefficients of the graphical representation of the VAR. The sparsity-based precision matrix estimator is deduced from the D-trace loss with convex and nonconvex penalty functions. We establish the consistency of the penalized estimator and provide the conditions for which all true zero entries of the precision matrix are actually estimated as zero with probability tending to one. The relevance of the method is supported by simulated experiments and a real data application.