Discrimination between nonstationary and nearly nonstationary processes and its effect on forecasting

The authors present theoretical and empirical evidence to show that the structure, for the observed serial dependence between the values of a series realisation, is quite sensitive to the distinction between a near-nonstationary model and a just nonstationary approximation to it. Reliable discrimination between the two may well be possible then, in practice, and this implies that improved modelling, as judged by increased forecasting effectiveness, can perhaps be achieved. The authors study exact and approximate measures of serial covariance and serial correlation, respectively, for a wide class of non-explosive linear time processes, including the ARMA and ARIMA models.