A further note on the stationarity and invertibility restraints on the parameters of mixed autoregressive moving average processes

Summary

It is well known that, for a gaussian process to be stationary, it is necessary and sufficient that the infinite order autocovariance matrix should be positive definite. This fact can be used to obtain the stationarity conditions, for a general autoregressive process; and, hence, the stationarity and invertibility conditions, for any mixed autoregressive moving average process. An interesting connection with a recently reported recursive approach is also noted.