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Higher-order asymptotic expansions of the least-squares estimation bias in first-order dynamic regression models

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  • Kiviet, Jan F.
  • Phillips, Garry D.A.

Abstract

An approximation to order T−2 is obtained for the bias of the full vector of least-squares estimates obtained from a sample of size T in general stable but not necessarily stationary ARX(1) models with normal disturbances. This yields generalizations, allowing for various forms of initial conditions, of Kendall’s and White’s classic results for stationary AR(1) models. The accuracy of various alternative approximations is examined and compared by simulation for particular parameterizations of AR(1) and ARX(1) models. The results show that often the second-order approximation is considerably better than its first-order counterpart and hence opens up perspectives for improved bias correction. However, order T−2 approximations are also found to be more vulnerable in the near unit root case than the much simpler order T−1 approximations.

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Bibliographic Info

Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

Volume (Year): 56 (2012)
Issue (Month): 11 ()
Pages: 3705-3729

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Handle: RePEc:eee:csdana:v:56:y:2012:i:11:p:3705-3729

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Keywords: ARX-model; Asymptotic expansion; Bias approximation; Lagged dependent variable; Monte Carlo simulation;

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References

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  1. Hadri, Kaddour & Phillips, Garry D. A., 1999. "The accuracy of the higher order bias approximation for the 2SLS estimator," Economics Letters, Elsevier, vol. 62(2), pages 167-174, February.
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  7. Dufour, J.M. & Kiviet, J.F., 1995. "Exact Tests in Single Equation Autoregressive Distributed Lag Models," Cahiers de recherche, Universite de Montreal, Departement de sciences economiques 9549, Universite de Montreal, Departement de sciences economiques.
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  10. Sawa, Takamitsu, 1978. "The exact moments of the least squares estimator for the autoregressive model," Journal of Econometrics, Elsevier, Elsevier, vol. 8(2), pages 159-172, October.
  11. Jan F. Kiviet & Garry D. A. Phillips, 2005. "Moment approximation for least-squares estimators in dynamic regression models with a unit root *," Econometrics Journal, Royal Economic Society, vol. 8(2), pages 115-142, 07.
  12. Orcutt, Guy H & Winokur, Herbert S, Jr, 1969. "First Order Autoregression: Inference, Estimation, and Prediction," Econometrica, Econometric Society, Econometric Society, vol. 37(1), pages 1-14, January.
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  16. Emma M. Iglesias & Garry D. A. Phillips, 2008. "Finite Sample Theory of QMLE in ARCH Models with Dynamics in the Mean Equation," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(4), pages 719-737, 07.
  17. Vinod, H.D. & Shenton, L.R., 1996. "Exact Moments for Autor1egressive and Random walk Models for a Zero or Stationary Initial Value," Econometric Theory, Cambridge University Press, vol. 12(03), pages 481-499, August.
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  25. repec:fth:exetec:99/06 is not listed on IDEAS
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Citations

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Cited by:
  1. Liu-Evans, Gareth, 2010. "An alternative approach to approximating the moments of least squares estimators," MPRA Paper 26550, University Library of Munich, Germany.
  2. Kiviet, Jan F. & Phillips, Garry D.A., 2014. "Improved variance estimation of maximum likelihood estimators in stable first-order dynamic regression models," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 76(C), pages 424-448.
  3. Jan F. Kiviet & Garry D. A. Phillips, 2000. "Improved Coefficient and Variance Estimation in Stable First-Order Dynamic Regression Models," Econometric Society World Congress 2000 Contributed Papers 0631, Econometric Society.
  4. Liu-Evans, Gareth, 2014. "A note on approximating moments of least squares estimators," MPRA Paper 57543, University Library of Munich, Germany.

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