The process of statistical model selection often involves comparison of quite distinct competing models, none of which is correct in any strict sense. In such situations, the classical, nested-model comparison procedures are inapplicable. This paper describes an easily calculated and broadly applicable graphical diagnostic for model comparison and also some robust generalizations to the time series situation of a test statistic of Vuong (1989) for non-nested model comparisons of incorrect models. After presenting some supporting theory, we illustrate the application of these new procedures by comparing ARIMA models with “structural” component models for forty seasonal economic time series, continuing a study by Bell and Pugh 1989) who used AIC for this purpose. When the comparison procedures are decisive, a RIMA models are usually favored.

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