On the prediction of multivariate arma processes with a time dependent covariance structure

The general m-variate ARMA model with time dependent coefficient matrices is considered to describe a process with time-dependent variance. A set of suitable AR and MA regularity conditions is given to ensure existence and uniqueness of second-order solutions of the model. A simple form of the above solution is expressed as a one sided moving average, in terms of one sided Green's matrices associated with the AR operator. Using these results we solve the prediction problem. A few examples are added to illustrate the general results.