Vector ARMA Time Series Models and Forecasting

Abstract

In this chapter, the vector autoregressive moving average (ARMA) models that were introduced in Section 1.2.2 are examined, and the stationarity and invertibility aspects of vector ARMA processes are considered. The covariance matrix structure of vector ARMA processes is considered, in general as well as for special cases such as first-order MA, AR, and ARMA models. In addition, consideration of parameter identifiability of mixed ARMA model representations is given. Nonstationary ARMA processes are also considered, and the concept of cointegration among the component series of a nonstationary process is introduced. Forecasting of vector ARMA models, including computation of forecasts and mean squared error matrix of the forecast errors, is presented.