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Estimation of the degree of differencing of an ARIMA process

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Summary

A method of estimating the degree of differencing of an ARIMA process is proposed. This is based on fitting an AR model to the original and to each differenced series and calculating the residual sum of squares. As an application, we suggest an identification method of an ARI (p, d) process combining our method of estimating the degree of differencing with Akaike's Information Criterion.

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References

  1. Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle, in2nd International Symposium on Information Theory, (eds. B. N. Petrov and F. Csáki), Budapest, Akadémia Kiado, 267–281.

    Google Scholar 

  2. Akaike, H. (1974). A new look at the statistical model identification,I.E.E.E. Trans. Auto. Control., AC-19, 716–723.

    Article  MathSciNet  Google Scholar 

  3. Anderson, O. D. (1975). A note on differencing autoregressive moving average (p, q) processes,Biometrika,62, 521–523.

    Article  MathSciNet  Google Scholar 

  4. Anderson, O. D. (1976).Time Series Analysis and Forecasting, The Box-Jenkins Approach, Butterworths, London.

    Google Scholar 

  5. Anderson, T. W. (1971).The Statistical Analysis of Time Series, Wiley, New York.

    MATH  Google Scholar 

  6. Billingsley, P. (1968).Convergence of Probability Measures, Wiley, New York.

    MATH  Google Scholar 

  7. Box, G. E. P. and Jenkins, G. M. (1976).Time Series Analysis, Forcecasting and Control (Revised ed.), Holden Day, San Francisco.

    Google Scholar 

  8. Grenander, U. and Rosenblatt, M. (1954). An extension of a theorem of G. Szegő and its application to the study of stochastic processes,Trans. Amer. Math. Soc.,76, 112–126.

    MathSciNet  MATH  Google Scholar 

  9. Hannan, E. J. (1980). The estimation of the order of an ARMA process,Ann. Statist.,8, 1071–1081.

    Article  MathSciNet  Google Scholar 

  10. Hasza, D. P. and Fuller, W. A. (1979). Estimation for autoregressive processes with unit roots,Ann. Statist.,7, 1106–1120.

    Article  MathSciNet  Google Scholar 

  11. Ozaki, T. (1977). On the order determination of ARIMA models,Appl. Statist.,26, 290–301.

    Article  Google Scholar 

  12. Shibata, R. (1976). Selection of the order of an autoregressive model by Akaike's information criterion,Biometrika,63, 117–126.

    Article  MathSciNet  Google Scholar 

  13. Yajima, Y. (1980). On an effect of overdifferencing on the prediction of ARIMA processes, inRecent Developments in Statistical Inference and Data Analysis, (ed. K. Matusita), North-Holland, Amsterdam, 335–345.

    Google Scholar 

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Authors and Affiliations

  1. Tokyo Institute of Technology, Tokyo, Japan

    Yoshihiro Yajima

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  1. Yoshihiro Yajima
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Yajima, Y. Estimation of the degree of differencing of an ARIMA process. Ann Inst Stat Math 37, 389–408 (1985). https://doi.org/10.1007/BF02481108

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  • DOI: https://doi.org/10.1007/BF02481108

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