*(English)*Zbl 0669.62085

The problems of regression and autoregressive model selection are closely related. One of the leading model selection methods is the Akaike information criterion AIC. But it tends to overfit the model what becomes evident when one examines plots of AIC and the actual Kullback-Leibler information for the various candidate models.

In this paper a bias-corrected version of AIC for nonlinear regression and autoregressive time series models is obtained. Monte Carlo results for linear regression model selection and for autoregressive model selection are presented. Amongst eight criteria (including Mallows Cp, the AIC criterion, the corrected AIC criterion $AI{C}_{C}$ and a criterion of Schwarz) the $AI{C}_{C}$ had the largest percentage of correct selection (96 and 88 %, respectively, for samples of size 10 and 20, respectively, in the linear regression case). $AI{C}_{C}$ seems to be preferable especially for small samples.