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Edgeworth Approximation of a Finite Sample Distribution for an AR(1) Model with Measurement Error
Department of Mathematical Sciences, Kwansei Gakuin University, Sanda, Japan
- 1 Department of Mathematical Sciences, Kwansei Gakuin University, Sanda, Japan
Open Journal of Statistics·Volume 02 (2012)·Pages 383–388·Published 30 October 2012·DOI10.4236/ojs.2012.24046
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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(T 1/2 ). 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.
KeywordsEdgeworth ExpansionOLSMeasurement ErrorInstrumental Variables Estimator
- 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
- 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
- W. A. Fuller, “Measurement Error Models,” John Wiley, New York, 1987. doi:10.1002/9780470316665
- 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
- 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
- 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
- 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
- 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
- J. D. Sargan, “Econometric Estimators and the Edgeworth Expansions,” Econometrica, Vol. 44, No. 3, 1976, pp. 421-448. doi:10.2307/1913972
- 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
- 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
- K. Hayakawa “A Note on Bias in First-Differenced AR(1) Models,” Economics Bulletin, Vol. 3 No. 27, 2006, pp. 1- 10.
- 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