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Efficient Estimation Using the Characteristic Function

Author

Listed:
  • Marine Carrasco

    (Université de Montréal, Départment d'Economie - CIREQ - Centre interuniversitaire de recherche en économie quantitative - Université de Montréal)

  • Rachidi Kotchoni

    () (THEMA - Théorie économique, modélisation et applications - UCP - Université de Cergy Pontoise - Université Paris-Seine - CNRS - Centre National de la Recherche Scientifique)

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 \alpha that needs to be selected. The aim of the present paper is to provide a way to optimally choose \alpha 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 fi nite sample dependence of the AMSE on \alpha . 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 \alpha. 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.

Suggested Citation

  • Marine Carrasco & Rachidi Kotchoni, 2013. "Efficient Estimation Using the Characteristic Function," Working Papers hal-00867850, HAL.
  • Handle: RePEc:hal:wpaper:hal-00867850
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00867850
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    References listed on IDEAS

    as
    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. Carrasco, Marine, 2012. "A regularization approach to the many instruments problem," Journal of Econometrics, Elsevier, vol. 170(2), pages 383-398.
    3. Linton, Oliver, 2002. "Edgeworth approximations for semiparametric instrumental variable estimators and test statistics," Journal of Econometrics, Elsevier, vol. 106(2), pages 325-368, February.
    4. 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.
    5. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    6. 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.
    7. 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.
    8. Peter C. B. Phillips & Hyungsik R. Moon, 1999. "Linear Regression Limit Theory for Nonstationary Panel Data," Econometrica, Econometric Society, vol. 67(5), pages 1057-1112, September.
    9. Buse, A, 1992. "The Bias of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 60(1), pages 173-180, January.
    10. 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, vol. 20(2), pages 198-212, April.
    11. 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.
    12. Ai[diaeresis]t-Sahalia, Yacine & Kimmel, Robert, 2007. "Maximum likelihood estimation of stochastic volatility models," Journal of Financial Economics, Elsevier, vol. 83(2), pages 413-452, February.
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    Cited by:

    1. Pierre Chaussé, 2011. "Generalized empirical likelihood for a continuum of moment conditions," Working Papers 1104, University of Waterloo, Department of Economics, revised Oct 2011.
    2. Da Fonseca José & Grasselli Martino & Ielpo Florian, 2014. "Estimating the Wishart Affine Stochastic Correlation Model using the empirical characteristic function," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 18(3), pages 1-37, May.
    3. repec:kap:compec:v:51:y:2018:i:2:d:10.1007_s10614-017-9692-6 is not listed on IDEAS
    4. Arellano, Manuel & Hansen, Lars Peter & Sentana, Enrique, 2012. "Underidentification?," Journal of Econometrics, Elsevier, vol. 170(2), pages 256-280.
    5. Kotchoni, Rachidi, 2012. "Applications of the characteristic function-based continuum GMM in finance," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3599-3622.

    More about this item

    Keywords

    Conditional moment restriction; Continuum of moment conditions; Generalized method of moments; Mean square error; Stochastic expansion; Tikhonov regularization;

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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