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The identification of ARMA processes

Published online by Cambridge University Press:  14 July 2016

An Hong-Zhi  and
Chen Zhao-Guo
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Abstract

This paper presents a review of recent results for the identification of ARMA processes according to the principles introduced by Akaike, i.e. assuming that the true orders exist and proposing criteria such as AIC and BIC. The development both of these methods and of consistency theory has been led by E. J. Hannan.

Keywords

AICBICESTIMATE OF ARMA ORDERSUBSET FITTINGSTRONG CONSISTENCY
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. 75 - 87
Copyright
Copyright © 1986 Applied Probability Trust 

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References

Akaike, H. (1969) Fitting autoregression models for prediction. Ann. Inst. Statist. Math. 21, 243–247.CrossRefGoogle Scholar
Akaike, H. (1973) Information theory and estimation of the maximum likelihood principle. In 2nd International Symposium on Information Theory, ed. Petrov, B. N. and Csaki, F., Akademiai Kiado, Budapest, 261–281.Google Scholar
Hong-Zhi, An, Zhao-Guo, Chen and Hannan, E. J. (1982) Autocorrelation, autoregression and autoregressive approximation. Ann. Statist. 10, 926–936.Google Scholar
Hong-Zhi, An and Lan, Gu (1985) On the selection of regression variables. Acta Math. Appl. Sinica, English Series 2 (1).Google Scholar
Anderson, T. W. (1977) Estimation for autoregressive moving average models in the time and frequency domain. Ann. Statist. 5, 842–856.Google Scholar
Box, G. E. P. and Jenkins, G. M. (1970) Time Series Analysis, Forecasting and Control. Holden Day, San Francisco.Google Scholar
Zhao-Guo, Chen (1985) On the recursive fitting of subset autoregressive-moving average process. Acta Math. Appl. Sinica B English Series 2 (1).Google Scholar
Lan, Gu and Hong-Zhi, An (1983) Fitting AR models by using partial parameters. Acta Math. Appl. Sinica A. To appear.Google Scholar
Hannan, E. J. (1970) Multiple Time Series. Wiley, New York.Google Scholar
Hannan, E. J. (1973) The asymptotic theory of linear time series models. J. Appl. Prob. 10, 130–145.CrossRefGoogle Scholar
Hannan, E. J. (1980) The estimation of the order of an ARMA series. Ann. Statist. 8, 1071–1081.Google Scholar
Hannan, E. J. and Kavalieris, L. (1983) The convergence of autocorrelations and autoregressions. Austral. J. Statist. 25, 287–297.Google Scholar
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
Hannan, E. J. and Rissanen, J. (1982) Recursive estimation of mixed autoregressive-moving average order. Biometrika 69, 81–94.Google Scholar
Shibata, R. (1976) Selection of the order of an autoregressive model by Akaike's information criterion. Biometrika 63, 117–126.CrossRefGoogle Scholar
Shou-Ren, Wang and Zhao-Guo, Chen (1985) Estimation of the order of ARMA model by linear procedures. Chinese Ann. Math. B 6, 53–70.Google Scholar
Whittle, P. (1963) On the fitting multivariate autoregression and the approximate canonical factorization of a spectral density matrix. Biometrika 50, 129–134.Google Scholar