Abstract.In this paper we examine the properties of Akaike's (Fitting autoregressive models for prediction,Ann. Inst. Statist. Math.21 (1969), 243–47) and Hannan and Quinn's (The determination of the order of an autoregression,J. R. Statist. Soc., Ser. B41 (1979), 190–95) information criteria in stationary autoregressive time series models when the true order of the process is greater than the maximum considered by the analyst. The limiting distributions of the estimated orders are derived and the implications of these results for model building are conside
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