Computation of vector ARMA autocovariances

This note describes an algorithm for computing the autocovariance sequence of a VARMA process, without requiring the intermediary step of determining the Wold representation. Although the recursive formula for the autocovariances is well-known, the initialization of this recursion in standard treatments (such as Brockwell and Davis (1991) or Lütkepohl (2007)) is slightly nuanced; we provide explicit formulas and algorithms for the initial autocovariances.