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Statistical forecasting for stochastic processes

  • Part II Inference For Stochastic Models
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Abstract

The main purpose of this paper is to review the efficiency properties of least-squares predictors when the parameters are estimated. It is shown that the criterion of asymptotic best unbiased predictors for general stochastic models is a natural analogue of the minimum mean-square error criterion used traditionally in linear prediction for linear models. The results are applied to log-linear models and autoregressive processes. Both stationary and non-stationary processes are considered.

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References

  1. T.W. Anderson, On asymptotic distribution of estimates of parameters of stochastic difference equations, Ann. Math. Statist. 30(1959)676.

    Google Scholar 

  2. I.V. Basawa, Asymptotic distributions of prediction errors and related tests of fit for nonstationary processes, Ann. Statist. (1986), to appear.

  3. I.V. Basawa and B.L.S. Prakasa Rao,Statistical Inference for Stochastic Processes (Academic Press, London, 1980).

    Google Scholar 

  4. I.V. Basawa, R.M. Huggins and R.G. Staudte, Robust tests for time series with an application to first-order autoregressive processes, Biometrika 72(1985)559.

    Google Scholar 

  5. J. Bibby and H. Toutenburg,Prediction and Improved Estimation in Linear Models (Wiley, New York, 1977).

    Google Scholar 

  6. G.E.P. Box and G.M. Jenkins,Time Series Analysis, 2nd Edition (Holden-Day, San Francisco, 1976).

    Google Scholar 

  7. W.A. Fuller and D.P. Hasza, Properties of predictors for autoregressive time series, J. Amer. Statist. Assoc. 76(1981)155.

    Google Scholar 

  8. A.S. Goldberger, Best linear unbiased prediction in the generalized linear regression model, J. Amer. Statist. Assoc. 57(1962)369.

    Google Scholar 

  9. K.S. Kaminski and P.I. Nelson, Best linear unbiased prediction of order statistics in location and scale families, J. Amer. Statist. Assoc. 70(1975)145.

    Google Scholar 

  10. P. McCullagh and J.A. Nelder,Generalized Linear Models (Chapman and Hall, London, 1983).

    Google Scholar 

  11. P. Whittle,Prediction and Regulation (Van Nostrand, Princeton, 1963).

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematical Statistics, La Trobe University, 3083, Bundoora, Victoria, Australia

    I. V. Basawa

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  1. I. V. Basawa
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Additional information

This paper is based on a “key note” lecture given at the meeting of The Institute of Management Sciences and the Operations Research Society of America, held in Williamsburg, Virginia, January 7–9, 1985.

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Basawa, I.V. Statistical forecasting for stochastic processes. Ann Oper Res 8, 133–149 (1987). https://doi.org/10.1007/BF02187087

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  • DOI: https://doi.org/10.1007/BF02187087

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