Diagnostic checks of non-standard time series models

Diagnostic checks have become a standard tool for helping to assess the adequacy of a forecasting system since Box and Jenkins' (1970) ARIMA modelling technique became popular. However, most of the research has developed checks for normal or second-order stationary models. This paper gives various diagnostic checks that can be performed simply on nonnormal, non-standard models such as the class of multiprocess models (Harrison and Stevens, 1976), where residuals are definitely not normal. The performance to date of these models can then be objectively scrutinized on-line. Examples, including a generalized cusum technique, are given to illustrate the effectiveness of the techniques on specific series.