A note on reparameterizing a vector autoregressive moving average model to enforce stationarity

We use the orrespondence between the partial autocorrelation matrices and the parameter matrices of a vector autoregression to obtain a new parameterization of a vector ARMA model that enforces the stationarity condition. We show how to go efficiently from the new parameterization ohe usual one. Thus the likelihood of observations from an ARMA model can easily be obtained using the new parameterization. In addition, for vector autoregressive models and scalar ARMA models, the new parameterization permits fast computation of the autocovariances of the model.