Vector autoregression process. Stationarity and simulation

Abstract

For vector discrete-parameter random autoregressive processes and for a mixed autoregression / moving-average model, we obtain conditions which should be satisfied by the correlation functions or the model coefficients in order that the process be weakly stationary. Fairly simple tests are used. Algorithms for modeling such vector stationary processes are given. Examples are presented clarifying testing criteria for stationarity of models defined in terms of the coefficients or the correlation functions of the process.