Statistical Papers

, Volume 30, Issue 1, pp 163–183 | Cite as

Small sample properties of estimators in the autocorrelated error model: a review and some additional simulations

  • Terry E. Dielman
  • Roger C. Pfaffenberger
Articles

Abstract

This paper provides a review of the literature concerning estimation in time series regression with first-order autocorrelated disturbances. Some additional simulation results confirm that the Cochrane-Orcutt estimator should not be used to correct for autocorrelation whether the explanatory variable is trended or not. Preferred estimators include a Bayesian estimator, full maximum likelihood and the iterative Prais-Winsten estimator.

Keywords

Generalize Little Square Bayesian Estimator Best Linear Unbiased Estimator Autocorrelated Error Generalize Little Square Estimator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Aitken, A. C. (1935). On least squares and linear combinations of observations. Proc. Royal Soc. Edinburgh 55: 42–48.Google Scholar
  2. Beach, C. and MacKinnon, J. (1978). A maximum likelihood procedure for regression models. J. Econometrics 13: 327–340.MathSciNetGoogle Scholar
  3. Chipman, J. S. (1979). Efficiency of least squares estimation of linear trend when residuals are autocorrelated. Econometrica 47: 115–128.MATHCrossRefMathSciNetGoogle Scholar
  4. Cochrane, D. and Orcutt, G. H. (1949). Application of least squares regression to relationships containing autocorrelated error terms. J. Amer. Statist. Assoc. 44: 32–61.MATHCrossRefGoogle Scholar
  5. Corradi, C. (1979). A note on the computation of maximum likelihood estimates in linear regression models with autocorrelated errors. J. Econometrics 11: 303–317.MATHCrossRefMathSciNetGoogle Scholar
  6. Dent, W. T. and Cassing, S. (1978). On modified maximum likelihood estimators of the autocorrelation coefficient in linear models. Biometrika 65: 211–213.MATHGoogle Scholar
  7. Dielman, T. and Pfaffenberger, R. (1989). Efficiency of ordinary least squares for linear models with autocorrelation. J. Amer. Statist. Assoc., forthcoming.Google Scholar
  8. Don, F. J. H. and Magnus, J. R. (1980). One the unbiasedness of iterated GLS estimators. Commun. Statist. A-Theory Meth. 9: 519–527.CrossRefMathSciNetGoogle Scholar
  9. Doran, H. E. (1981). Omission of an observation from a regression analysis: A discussion on efficiency loss with applications. J. Econometrics 16: 367–374.CrossRefGoogle Scholar
  10. Durbin, J. (1960). The fitting of time series models. Rev. Intern. Statist. Inst. 28: 233–243.CrossRefGoogle Scholar
  11. Durbin, J. and Watson, G. S. (1950). Testing for serial correlation in least squares regression I. Biometrika 37: 409–428.MATHMathSciNetGoogle Scholar
  12. Fomby, T. and Guilkey, D. (1978). On choosing the optimal level of significance for the Durbin-Watson test and the Bayesian alternative. J. Econometrics 8: 203–213.MATHCrossRefMathSciNetGoogle Scholar
  13. Glezakos, C. (1980). Autocorrelation and trended independent variables: A comment. Rev. Econom. Statist. 62: 484–487.CrossRefMathSciNetGoogle Scholar
  14. Goldberger, A. S. (1964). Econometric Theory. New York: Wiley.MATHGoogle Scholar
  15. Grenander, U. (1954). On the estimation of regression coefficients in the case of autocorrelated disturbances. Annals Math. Statist. 25: 252–272.CrossRefMathSciNetGoogle Scholar
  16. Griffiths, W. and Dao, D. (1980). A note on a Bayesian estimator with autocorrelated disturbances. J. Econometrics 12: 389–392.MATHCrossRefMathSciNetGoogle Scholar
  17. Gurland, J. (1954). An example of autocorrelated disturbances in linear regression. Econometrica 22: 218–227.MATHCrossRefMathSciNetGoogle Scholar
  18. Hildreth, C. (1969). Asymptotic distribution of maximum likelihood estimators in a linear model with autoregressive disturbances. Annals Math. Stat. 40: 583–594.CrossRefMathSciNetGoogle Scholar
  19. Hildreth C. and Dent, W. T. (1974). An adjusted maximum likelihood estimator of autocorrelation in disturbances. In Econometrics and Econometric Theory: Essays in Honour of J. Tinbergen. Ed. W. Sellekaerts. pp. 3–25. London: Macmillan.Google Scholar
  20. Hildreth, C. and Lu, J. Y. (1960). Demand relations with autocorrelated disturbances. Research Bulletin 276, Michigan State University Agricultural Experiment Station.Google Scholar
  21. Johnston, J. (1972). Econometric Methods. New York: McGraw-Hill.Google Scholar
  22. Kadiyala, K. R. (1968). A transformation used to circumvent the problem of autocorrelation. Econometrica 36: 93–96.MATHCrossRefGoogle Scholar
  23. Kendall, M. G. (1954). Note on bias in the estimation of autocorrelation. Biometrika 41: 403–404.MATHMathSciNetGoogle Scholar
  24. Kmenta, J. (1971). Elements of Econometrics. New York: Macmillan.MATHGoogle Scholar
  25. Kmenta, J. (1986). Elements of Econometrics, 2nd Edition. New York: Macmillan Publishing Co.Google Scholar
  26. Kobayashi, M. (1985). Comparison of efficiencies of several estimatiors for linear regressions with autocorrelated errors. J. Amer. Statist. Assoc. 75: 1005–1009.Google Scholar
  27. Maddala, G. S. (1977). Econometrics. New York: McGraw-Hill.MATHGoogle Scholar
  28. Maeshiro, A. (1976). Autoregressive transformation, trended independent variables and autocorrelated disturbance terms. Rev. Econom. Statist. 58: 497–500.CrossRefGoogle Scholar
  29. Maeshiro, A. (1979). On the retension of the first observaton in serial correlation adjustment of regression models. Intern. Econom. Rev. 20: 259–265.MATHCrossRefGoogle Scholar
  30. Maeshiro, A. (1980) Autocorrelation and trended explanatory variables: A reply. Intern. Econom. Rev. 20: 487–489.Google Scholar
  31. Magee, L. (1987). A note on Cochrane-Orcutt estimation. J. Econometrics 35: 211–218.MATHCrossRefMathSciNetGoogle Scholar
  32. Malinvaud, E. (1966). Statistical Methods of Econometrics. Chicago: Rand McNally.MATHGoogle Scholar
  33. Oberhofer, W. and Kmenta, J. (1974). A general procedure for obtaining maximum likelihood estimates in generalized regression models. Econometrica 42: 579–590.MATHCrossRefMathSciNetGoogle Scholar
  34. Park, R. and Mitchell G. (1980). Estimating the autocorrelated error model with trended data. J. of Econometrics 13: 185–201.MATHCrossRefGoogle Scholar
  35. Porrier, D. (1987). The effect of the first observation in regression models with first-order autoregressive disturbance. J. Royal Satist. Soc., Ser. C. 27: 67–68.Google Scholar
  36. Prais, S. J. and Winsten, C. B. (1954). Trend estimators and serial correlation. Cowles Commission Discussion Paper: Stat No. 383, Chicago.Google Scholar
  37. Rao, P. and Griliches, E. (1969). Small sample properties of several two-stage regression methods in the context of autocorrelated errors. J. Amer. Statist. Assoc. 64: 253–272.CrossRefGoogle Scholar
  38. Sargan, J. D. (1964). Wages and prices in the United Kingdom: A study in econometric methodology. In Econometric Analysis for National Economic Planning. Eds. P. E. Hart G. Mills and J. K. Whitaker. pp. 25–63. London: Butterworths.Google Scholar
  39. Spitzer, J. (1979). Small sample properties of nonlinear least squares and maximum likelihood estimation in the context of autocorrelated errors. J. Amer. Statist. Assoc. 74: 41–47.CrossRefGoogle Scholar
  40. Taylor, W. E. (1981). On the efficiency of the Cochrane-Orcutt estimator. J. Econometrics 17: 67–82.MATHCrossRefMathSciNetGoogle Scholar
  41. Thornton, D. L. (1987). A note on the efficiency of the Cochrane-Orcutt estimator of the AR(1) regression model. J. Econometrics, 36: 369–376.MATHCrossRefMathSciNetGoogle Scholar
  42. Watson, G. S. (1955). Serial correlation in regression analysis I. Biometrika 42: 327–341.MATHMathSciNetGoogle Scholar
  43. Zellner, A. (1971). An Introduction to Bayesian Inference in Econometrics. New York: Wiley.MATHGoogle Scholar
  44. Zellner, A. and Tiao, G. (1964). Bayesian analysis of the regression model with autocorrelated errors. J. Amer. Statist. Assoc. 59: 763–778.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Terry E. Dielman
    • 1
  • Roger C. Pfaffenberger
    • 1
  1. 1.M. J. Neeley School of BusinessTexas Christian UniversityFort Worth

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