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Consistency of model selection and parameter estimation

Published online by Cambridge University Press:  14 July 2016

Ritei Shibata
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Abstract

The relationship between consistency of model selection and that of parameter estimation is investigated. It is shown that the consistency of model selection is achieved at the cost of a lower order of consistency of the resulting estimate of parameters in some domain. The situation is different when selecting autoregressive moving average models, since the information matrix becomes singular when overfitted. Some detailed analyses of the consistency are given in this case.

Keywords

AUTOREGRESSIVE PROCESSESAKAIKE INFORMATION CRITERIONFINITE PARAMETER ESTIMATION
Type
Part 2—Estimation for Time Series
Information
Journal of Applied Probability , Volume 23 , Issue A: Essays in Time Series and Allied Processes , 1986 , pp. 127 - 141
Copyright
Copyright © 1986 Applied Probability Trust 

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References

[1] Akaike, H. (1970) Statistical predictor identification. Ann. Inst. Statist. Math. 22, 203–217.CrossRefGoogle Scholar
[2] Akaike, H. (1973) Information theory and an extension of the maximum likelihood principle. In 2nd Int. Symposium on Information Theory , ed. Petrov, B. N. and Csáki, F., Akadémia Kiado, Budapest, 267–281.Google Scholar
[3] Chen, Zhao-Guo (1984) The asymptotic efficiency of a linear procedure of estimation for ARMA models. J. Time Series Anal. CrossRefGoogle Scholar
[4] Hannan, E. J. (1980) The estimation of the order of an ARMA process Ann. Statist. 8, 1071–1081.CrossRefGoogle Scholar
[5] Hannan, E. J. (1982) Testing for autocorrelation and Akaike's criterion. In Essays in Statistical Science: Papers in Honour of P. A. P. Moran , ed. Gani, J. M. and Hannan, E. J., Applied Probability Trust, Sheffield, 403–412.Google Scholar
[6] Hannan, E. J. (1982) Fitting multivariate ARMA models. In Statistics and Probability, Essays in Honour of C. R. Rao , ed. Kallianpur, G., Krishnaiah, P. R. and Ghosh, J. K., North-Holland, Amsterdam, 307–316.Google Scholar
[7] Hannan, E. J. and Quinn, B. G. (1979) The determination of the order of an autoregression. J. R. Statist. Soc. B 41, 190–195.Google Scholar
[8] Hannan, E. J. and Rissanen, J. (1982) Recursive estimation of mixed autoregressive-moving average order. Biometrika 69, 81–94.CrossRefGoogle Scholar
[9] Mallows, C. L. (1973) Some comments on Cp. Technometrics 15, 661–675.Google Scholar
[10] Schwarz, G. (1978) Estimating the dimension of a model. Ann. Statist. 6, 461–464.CrossRefGoogle Scholar
[11] Shibata, R. (1976) Selection of the order of an autoregressive model by Akaike's information criterion. Biometrika 63, 117–126.CrossRefGoogle Scholar
[12] Shibata, R. (1977) Convergences of least squares estimates of autoregressive parameters. Austral. J. Statist. 19, 226–235.CrossRefGoogle Scholar
[13] Shibata, R. (1980) Asymptotically efficient selection of the order of the model for estimating parameters of a linear process. Ann. Statist. 8, 147–164.CrossRefGoogle Scholar
[14] Shibata, R. (1983) A theoretical view of the use of AIC. In Time Series Analysis: Theory and Practice 4, ed. Anderson, O. D., Elsevier, Amsterdam, 237–244.Google Scholar
[15] Shibata, R. (1984) Identification and selection of ARMA models. Tech. Rep. RT-MAE-8406, Institute of Mathematics and Statistics, University of São Paulo.Google Scholar