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Edgeworth Expansion for the OLS Estimator in a Time Series Regression Model

Published online by Cambridge University Press:  18 October 2010

Koichi Maekawa
Koichi Maekawa
Affiliation:
Hiroshima University
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Abstract

In this paper we consider the situation in which ordinary least squares (OLS) is used to estimate an ARMA (1,1) model with one exogenous variable. Applying Edgeworth expansion techniques, we examine the misspecification errors and the approximate distributions of the OLS estimator. Extensive numerical studies were performed and selected results are shown graphically. In addition, a technical device is developed to calculate the Edgeworth coefficients.

Type
Articles
Information
Econometric Theory , Volume 1 , Issue 2 , August 1985 , pp. 223 - 239
Copyright
Copyright © Cambridge University Press 1985

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References

REFERENCES

1.Fujikoshi, Y. and Ochi, Y.Asymptotic properties of the maximum likelihood estimate in the first order autoregressive process. Annals of the Institute of Statistical Mathematics 36 (1984): 119–128.CrossRefGoogle Scholar
2.Hannan, E. J.Multiple Time Series. New York, Wiley, 1970.CrossRefGoogle Scholar
3.Maekawa, K.An approximation to the distribution of the least squares estimator in an autoregressive model with exogenous variables, Econometrica 51 (1983): 229–238.CrossRefGoogle Scholar
4.Maekawa, K.Edgeworth expansions of the least squares estimator in ARMA (1,1) model with exogenous variables. The Hiroshima Economic Review 1 (1983): 57–78.Google Scholar
5.Maekawa, K. Edgeworth expansion for OLS estimator in an ARMAX model. Technical Report No. 122, Statistical Research Group, Hiroshima University, 1984.Google Scholar
6.Phillips, P.C.B.Approximations to some finite sample distributions associated with a first order stochastic difference equation, Econometrica 45 (1977): 463–485.CrossRefGoogle Scholar
7.Phillips, P.C.B.Edgeworth and saddle point approximations in the first order noncircular autoregression, Biometrika 65 (1978): 91–98.CrossRefGoogle Scholar
8.Phillips, P.C.B.Finite sample theory and the distribution s of alternative estimators of marginal propensity to consume. Review of Economic Studies XLVLL (1980): 183–224.CrossRefGoogle Scholar
9.Sargan, J. D.Econometric estimators and Edgeworth expansions. Econometrica 44 (1976): 421–448.CrossRefGoogle Scholar
10.Tanaka, K.Asymptotic expansions associated with the AR(1) model with unknown mean. Econometrica 51 (1983): 1221–1231.CrossRefGoogle Scholar
11.Tanaka, K.An asymptotic expansion associated with the maximum likelihood estimators in ARMA models. Journal of the Royal Statistical Society B 46 (1984): 58–67.Google Scholar
12.Taniguchi, M.On the second order asymptotic efficiency of estimators of Gaussian ARMA process. The Annals of Statistics 11 (1983): 157–169.CrossRefGoogle Scholar
13.Taniguchi, M.The third order asymptotic properties of maximum likelihood estimators for Gaussian processes. To appear in Journal of Multivariate Analysis (1985).Google Scholar
14.Tse, Y. K.Edgeworth approximations in a first order stochastic difference equation with exogenous variables. Journal of Econometrics 20 (1982): 175–195.CrossRefGoogle Scholar