Markov-Chain Approximations of Vector Autoregressions: Application of General Multivariate-Normal Integration Techniques

Abstract

Discrete Markov chains can be useful to approximate vector autoregressive processes for economists doing computational work. One such approximation method first presented by Tauchen (1986) operates under the general theoretical assumption of a transformed VAR with diagonal covariance structure for the process error term. We demonstrate one simple method of more conveniently treating this approximation problem in practice using readily available multivariate-normal integration techniques to allow for arbitrary positive-semidefinite covariance structures. Examples are provided using processes with non-diagonal and singular non-diagonal error covariances.