The Covariance Structure of Mixed ARMA Models

The purpose of this paper is to examine the covariance structure of mixed ARMA models, as discussed in Granger and Morris (1976). The method we use to obtain the autocovariances is based on the Wold representation of an ARMA model as it is given in Pandit (1973) or in Karanasos (2000). We give two examples to illustrate our general results: (i) two ARMA(2,2) processes with identical autoregressive polynomials and different moving average ones, and (ii) two ARMA(2,1) processes with different autoregressive and moving average polynomials.