OJS  Vol.2 No.4 , October 2012
Edgeworth Approximation of a Finite Sample Distribution for an AR(1) Model with Measurement Error
Author(s) Shuichi Nagata*
ABSTRACT
In this paper, we consider the finite sample property of the ordinary least squares (OLS) estimator for an AR(1) model with measurement error. We present the Edgeworth approximation for a finite distribution of OLS up to O(T1/2). We introduce an instrumental variable estimator that is consistent in the presence of measurement error. Finally, a simulation study is conducted to assess the theoretical results and to compare the finite sample performances of these estimators.

Cite this paper
S. Nagata, "Edgeworth Approximation of a Finite Sample Distribution for an AR(1) Model with Measurement Error," Open Journal of Statistics, Vol. 2 No. 4, 2012, pp. 383-388. doi: 10.4236/ojs.2012.24046.
References
[1]   F. H. C. Marriott and J. A. Pope, “Bias in the Estimation of Autocorrelations,” Biometrika, Vol. 41, No. 3-4, 1954, pp. 390-402. doi:10.2307/2332719

[2]   M. G. Kendall, “Note on the Bias in the Estimation of Autocorrelation,” Biometrika, Vol. 41, No. 3-4, 1954, pp. 403-404. doi:10.2307/2332720

[3]   W. A. Fuller, “Measurement Error Models,” John Wiley, New York, 1987. doi:10.1002/9780470316665

[4]   J. Staudenmayer and P. Buonaccorsi, “Measurement Error in Linear Autoregressive Model,” Journal of the American Statistical Association,” Vol. 100, No. 471. 2005, pp. 841-851. doi:10.1198/016214504000001871

[5]   K. Tanaka, “A Unified Approach to the Measurement Error Problem in Time Series Models,” Econometric Theory, Vol. 18, No. 2, 2002, pp. 278-296. doi: 10.1017/S026646660218203X

[6]   P. C. B. Phillips, “Approximations to Some Sample Distributions Associated with a First Order Stochastic Difference Equation,” Econometrica, Vol. 45, No. 2, 1977, pp. 463-485. doi.org/10.2307/1911222

[7]   K. Tanaka, “Asymptotic Expansions Associated with the AR(1) Model with Unknown Mean,” Econometrica, Vol. 51, No. 4, 1983, pp. 1221-1231. doi:10.2307/1912060

[8]   K. Maekawa “An Approximation to the Distribution of the Least Squares Estimator in an Autoregressive Model with Exogenous Variables,” Econometrica, Vol. 51, No.1, 1983, pp. 229-238. doi:10.2307/1912258

[9]   J. D. Sargan, “Econometric Estimators and the Edgeworth Expansions,” Econometrica, Vol. 44, No. 3, 1976, pp. 421-448. doi:10.2307/1913972

[10]   C. W. J. Granger and M. J. Morris, “Time Series Modeling and Interpretation,” Journal of the Royal Statistical Society A, Vol. 139, No. 2, 1976, pp. 246-257. doi:10.2307/2345178

[11]   K. Maekawa “Edgeworth Expansion for the OLS Estimator in a Time Series Regression Model,” Econometric Theory, Vol. 1, No. 2, 1985, pp. 223-239. doi:10.1017/S0266466600011154

[12]   K. Hayakawa “A Note on Bias in First-Differenced AR(1) Models,” Economics Bulletin, Vol. 3 No. 27, 2006, pp. 1- 10.

[13]   P. C. B. Phillips and C. Han, “Gaussian Inference in AR(1) Times Series with or without Unit Root,” Econometric Theory, Vol. 24, No. 3, 2008, pp. 631-650. doi:10.1017/S0266466608080262

 
 
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