The discrimination between autoregressive and moving average models from the estimated inverse correlations (Q1113247)

Autoregressive and moving average models may be discriminated between by selecting the model which minimises the information criterion, T log \({\hat \sigma}{}^ 2_ s+2s\), where \({\hat \sigma}{}^ 2_ s\) is the maximum likelihood estimate of the variance of the innovations, \(\epsilon_ t\), and s is the number of estimated parameters. It is suggested, instead, that for a moving average model \({\hat \sigma}{}^ 2_ s\) be computed from the autoregressive estimates of the inverse correlation function, and that an extension - called the \(FPE_{\alpha}\) criterion - of the information criterion is employed for the discrimination. The asymptotic behaviour of the proposed discrimination procedure is examined, and its finite sample behaviour is investigated by means of a simulation study. Applications to fields from batch chemical processes; refrigerator sales series; chemical process concentration readings and the Beveridge wheat price index are discussed.