© 1990 by Biometrika Trust
Improved estimators of Kullback–Leibler information for autoregressive model selection in small samples
Department of Statistics and Operations Research, New York University 40 West Fourth Street, New York, New York 10003, U.S.A.
Division of Statistics, University of California Davis, California 95616, U.S.A.
A new estimator, AICl, of the Kuliback-Leibler information is proposed for Gaussian autoregressive time series model selection. The expected information is decomposed into two terms, the first being estimated without bias. The second term is a penalty function which depends only weakly on the model parameters, and hence can be tabulated by simulation from a white noise process. The estimated information, AICl, is very nearly unbiased when the model is either correct or overfitted. It is shown that the penalty term of AICl, is asymptotically equivalent to that of the AICC criterion of Hurvich & Tsai (1989). For autoregressive models estimated from small samples by Burg's method, simulation provides strong support for the use of the simpler criterion AICC, perhaps using an unbiased version of the first term. If the autoregressive models are estimated by maximum likelihood, then: (a) if none of the candidate model dimensions exceeds one-half the sample size, AICl provides somewhat better model selections than AICc; (b) if some of the candidate models have large dimension, a case considered particularly in engineering applications, then AICl provides much better model selections in small samples than AICC.
Key Words: AIC • AICC • Kullback-Leibler information • Time series