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Local GMM Estimation of Time Series Models with Conditional Moment Restrictions

This paper investigates statistical properties of the local GMM (LGMM) estimator for some time series models defined by conditional moment restrictions. First, we consider Markov processes with possible conditional heteroskedasticity of unknown form and establish the consistency, asymptotic normality, and semi-parametric efficiency of the estimator. Second, inspired by simulation results showing that the LGMM estimator has a significantly smaller bias than the OLS estimator, we undertake a higher-order asymptotic expansion and analyze the bias properties of the LGMM estimator. The structure of the asymptotic expansion of the LGMM estimator reveals an interesting contrast with the OLS estimator that helps to explain the bias reduction in the LGMM estimator. The practical importance of these findings is evaluated in terms of a bond and option pricing exercise based on a diffusion model for spot interest rate.

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File URL: http://alcor.concordia.ca/~gospodin/research/cel_ar.pdf
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Paper provided by Concordia University, Department of Economics in its series Working Papers with number 08010.

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Length: 33 pages
Date of creation: Dec 2008
Date of revision:
Handle: RePEc:crd:wpaper:08010
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  13. Whitney K. Newey & Richard J. Smith, 2004. "Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators," Econometrica, Econometric Society, vol. 72(1), pages 219-255, 01.
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  15. Carrasco, Marine & Florens, Jean-Pierre, 2003. "On the Asymptotic Efficiency of GMM," IDEI Working Papers 173, Institut d'Économie Industrielle (IDEI), Toulouse.
  16. Peter C.B. Phillips & Jun Yu, 2003. "Jackknifing Bond Option Prices," Cowles Foundation Discussion Papers 1392, Cowles Foundation for Research in Economics, Yale University.
  17. Chen, Song Xi & Härdle, Wolfgang & Kleinow, Torsten, 2000. "An empirical likelihood goodness-of-fit test for time series," SFB 373 Discussion Papers 2001,1, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  18. van Giersbergen, Noud P.A., 2005. "On the effect of deterministic terms on the bias in stable AR models," Economics Letters, Elsevier, vol. 89(1), pages 75-82, October.
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  24. Carrasco, Marine & Florens, Jean-Pierre, 2000. "Generalization Of Gmm To A Continuum Of Moment Conditions," Econometric Theory, Cambridge University Press, vol. 16(06), pages 797-834, December.
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