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Efficient estimation using the Characteristic Function

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  • Marine Carrasco

    ()

  • Rachidi Kotchoni

Abstract

The method of moments proposed by Carrasco and Florens (2000) permits to fully exploit the information contained in the characteristic function and yields an estimator which is asymptotically as efficient as the maximum likelihood estimator. However, this estimation procedure depends on a regularization or tuning parameter å that needs to be selected. The aim of the present paper is to provide a way to optimally choose å by minimizing the approximate mean square error (AMSE) of the estimator. Following an approach similar to that of Newey and Smith (2004), we derive a higher-order expansion of the estimator from which we characterize the finite sample dependence of the AMSE on å. We provide a data-driven procedure for selecting the regularization parameter that relies on parametric bootstrap. We show that this procedure delivers a root T consistent estimator of å. Moreover, the data-driven selection of the regularization parameter preserves the consistency, asymptotic normality and efficiency of the CGMM estimator. Simulation experiments based on a CIR model show the relevance of the proposed approach.

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Bibliographic Info

Paper provided by CIRANO in its series CIRANO Working Papers with number 2013s-22.

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Date of creation: 01 Jul 2013
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Handle: RePEc:cir:cirwor:2013s-22

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Keywords: Conditional moment restriction; continuum of moment conditions; generalized method of moments; mean square error; stochastic expansion; Tikhonov regularization;

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References

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  1. Pascal Lavergne & Valentin Patilea, 2008. "Smooth Minimum Distance Estimation and Testing in Conditional Moment Restrictions Models: Uniform in Bandwidth Theory," Discussion Papers dp08-08, Department of Economics, Simon Fraser University.
  2. Jiang, George J & Knight, John L, 2002. "Estimation of Continuous-Time Processes via the Empirical Characteristic Function," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 20(2), pages 198-212, April.
  3. Jacho-Chávez, David Tomás, 2010. "Optimal Bandwidth Choice For Estimation Of Inverse Conditional–Density–Weighted Expectations," Econometric Theory, Cambridge University Press, vol. 26(01), pages 94-118, February.
  4. Oliver Linton, 2000. "Edgeworth approximations for semiparametric instrumental variable estimators and test statistics," LSE Research Online Documents on Economics, London School of Economics and Political Science, LSE Library 2156, London School of Economics and Political Science, LSE Library.
  5. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, Econometric Society, vol. 50(4), pages 1029-54, July.
  6. Carrasco, Marine, 2012. "A regularization approach to the many instruments problem," Journal of Econometrics, Elsevier, Elsevier, vol. 170(2), pages 383-398.
  7. Peter C.B. Phillips & Hyungsik R. Moon, 1999. "Linear Regression Limit Theory for Nonstationary Panel Data," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1222, Cowles Foundation for Research in Economics, Yale University.
  8. Koenker, Roger & Machado, José A.F. & Skeels, Christopher L. & Welsh, Alan H., 1994. "Momentary Lapses: Moment Expansions and the Robustness of Minimum Distance Estimation," Econometric Theory, Cambridge University Press, vol. 10(01), pages 172-197, March.
  9. Donald W.K. Andrews, 1988. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
  10. Ai[diaeresis]t-Sahalia, Yacine & Kimmel, Robert, 2007. "Maximum likelihood estimation of stochastic volatility models," Journal of Financial Economics, Elsevier, Elsevier, vol. 83(2), pages 413-452, February.
  11. 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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Cited by:
  1. Kotchoni, Rachidi, 2012. "Applications of the characteristic function-based continuum GMM in finance," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 56(11), pages 3599-3622.
  2. Pierre Chaussé, 2011. "Generalized empirical likelihood for a continuum of moment conditions," Working Papers 1104, University of Waterloo, Department of Economics, revised Oct 2011.

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