Serial Dependence Properties of Linear Processes

The paper describes a class of models rather more general than the ARIMA processes of Box and Jenkins, and surveys recently achieved results for their serial dependence behaviour. These properties are obtained analytically, from simulation and by direct computation-either approximately or exactly. The paper concentrates on the expectations of serial covariances and the problem of distinguishing between nearly non-stationary models and homogeneous non-stationary approximations to them-in particular, for a specific pair of ARMA(1,1) and IMA(1,1) processes.