Analysis of Regressions Containing Serially Correlated and Serially Uncorrelated Error Components

In time-series modeling, statisticians and econometricians have typically assumed that disturbances are generated by either the AR(p) process or the MA(q) process; both are intended to allow for a possible serial correlation in the disturbances. Recently, there has been a resurgence of interest in measurement errors which has drawn some attention to models with ''composite'' disturbances. This disturbance structure arises in dynamic models, e.g., when the true values of the dependent variables are unobservable but observed in the ''usual'' errors-in-variables fashion.A regression model is considered whose disturbance is additive in 2 independent components, one of which is serially uncorrelated and the other follows an AR(p) process. When properly transformed, the disturbance of the resulting model is again additive in 2 independent components, one of which is serially uncorrelated and the other follows an MA(p) scheme. In either form, the model is seen as a variant of some familiar error-component models.