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THE APPROXIMATE MOMENTS OF THE LEAST SQUARES ESTIMATOR FOR THE STATIONARY AUTOREGRESSIVE MODEL UNDER A GENERAL ERROR DISTRIBUTION

Published online by Cambridge University Press:  14 May 2007

Yong Bao
Yong Bao
Affiliation:
Temple University
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Abstract

I derive the approximate bias and mean squared error of the least squares estimator of the autoregressive coefficient in a stationary first-order dynamic regression model, with or without an intercept, under a general error distribution. It is shown that the effects of nonnormality on the approximate moments of the least squares estimator come into play through the skewness and kurtosis coefficients of the nonnormal error distribution.The author is grateful to the co-editor Paolo Paruolo and two anonymous referees for helpful comments. The author is solely responsible for any remaining errors.

Type
NOTES AND PROBLEMS
Information
Econometric Theory , Volume 23 , Issue 5 , October 2007 , pp. 1013 - 1021
Copyright
© 2007 Cambridge University Press

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References

REFERENCES

Abadir, K.M. & K. Hadri (2000) Is more information a good thing? Bias nonmonotonicity in stochastic difference equations. Bulletin of Economic Research 52, 91–100.Google Scholar
Abadir, K.M. & A. Lucas (2004) A comparison of minimum MSE and maximum power for the nearly integrated non-Gaussian model. Journal of Econometrics 119, 45–71.Google Scholar
Bao, Y. & A. Ullah (2006a) The second-order bias and mean squared error of estimators in time series models. Journal of Econometrics, forthcoming.Google Scholar
Bao, Y. & A. Ullah (2006b) Expectation of quadratic forms in normal and nonnormal variables with econometric applications. Working paper, University of Texas at San Antonio and University of California, Riverside.
Chandra, R. (1983) Estimation of Econometric Models when Disturbances are not Necessarily Normal. Ph.D. Dissertation, Department of Statistics, Lucknow University, India.
Copas, J.B. (1966) Monte Carlo results for estimation in a stable Markov time series. Journal of the Royal Statistical Society Series A 129, 110–116.Google Scholar
Evans, G.B.A. & N.E. Savin (1984) Testing for unit roots: 2. Econometrica 52, 1241–1270.Google Scholar
Grubb, D. & J. Symons (1987) Bias in regression with a lagged dependent variable. Econometric Theory 3, 371–386.Google Scholar
Hurwicz, L. (1950) Least-squares bias in time series. In T.C. Koopmans (ed.) Statistical Inference in Dynamic Economic Models, pp. 365–383. Wiley.
Kiviet, J.F. & G.D.A. Phillips (1993) Alternative bias approximations in regressions with a lagged dependent variable. Econometric Theory 9, 62–80.Google Scholar
Nagar, A.L. (1959) The bias and moment matrix of the general k-class estimators of the parameters in simultaneous equations. Econometrica 27, 575–595.Google Scholar
Peters, T.A. (1989) The exact moments of OLS in dynamic regression models with non-normal errors. Journal of Econometrics 40, 279–305.Google Scholar
Phillips, P.C.B. (1977) Approximations to some finite sample distributions associated with a first-order stochastic difference equations. Econometrica 45, 463–485.Google Scholar
Sawa, T. (1978) The exact moments of the least squares estimator for the autoregressive model. Journal of Econometrics 8, 159–172.Google Scholar
Shenton, L.R. & W.L. Johnson (1965) Moments of a serial correlation coefficient. Journal of the Royal Statistical Society Series B 27, 308–320.Google Scholar
Ullah, A. (2004) Finite Sample Econometrics. Oxford University Press.
Ullah, A., V.K. Srivastava, & R. Chandra (1983) Properties of shrinkage estimators when the disturbances are not normal. Journal of Econometrics 21, 389–402.Google Scholar
White, J.S. (1957) Approximate moments for the serial correlation coefficient. Annals of Mathematical Statistics 28, 798–802.Google Scholar
White, J.S. (1961) Asymptotic expansions of the mean and variance of the serial correlation coefficient. Biometrika 48, 85–94.Google Scholar