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Estimating mixtures of normal distributions via empirical characteristic function

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  • Kien Tran

Abstract

This paper uses the empirical characteristic function (ECF) procedure to estimate the parameters of mixtures of normal distributions. Since the characteristic function is uniformly bounded, the procedure gives estimates that are numerically stable. It is shown that, using Monte Carlo simulation, the finite sample properties of th ECF estimator are very good, even in the case where the popular maximum likelihood estimator fails to exist. An empirical application is illustrated using the monthl excess return of the Nyse value-weighted index.

Suggested Citation

  • Kien Tran, 1998. "Estimating mixtures of normal distributions via empirical characteristic function," Econometric Reviews, Taylor & Francis Journals, vol. 17(2), pages 167-183.
    • Handle: RePEc:taf:emetrv:v:17:y:1998:i:2:p:167-183
    DOI: 10.1080/07474939808800410
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    References listed on IDEAS

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    1. Kon, Stanley J, 1984. "Models of Stock Returns-A Comparison," Journal of Finance, American Finance Association, vol. 39(1), pages 147-165, March.
    2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. Kiefer, Nicholas M, 1978. "Discrete Parameter Variation: Efficient Estimation of a Switching Regression Model," Econometrica, Econometric Society, vol. 46(2), pages 427-434, March.
    4. Schmidt, Peter, 1982. "An Improved Version of the Quandt-Ramsey MGE Estimator for Mixtures of Normal Distributions and Switching Regressions," Econometrica, Econometric Society, vol. 50(2), pages 501-516, March.
    5. Phillips, Robert F., 1991. "A constrained maximum-likelihood approach to estimating switching regressions," Journal of Econometrics, Elsevier, vol. 48(1-2), pages 241-262.
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    Cited by:

    1. Carol Alexander & Sujit Narayanan, 2001. "Option Pricing with Normal Mixture Returns: Modelling Excess Kurtosis and Uncertanity in Volatility," ICMA Centre Discussion Papers in Finance icma-dp2001-10, Henley Business School, University of Reading, revised Dec 2001.
    2. Tsionas, Mike, 2012. "Simple techniques for likelihood analysis of univariate and multivariate stable distributions: with extensions to multivariate stochastic volatility and dynamic factor models," MPRA Paper 40966, University Library of Munich, Germany, revised 20 Aug 2012.
    3. Dinghai Xu, 2009. "The Applications of Mixtures of Normal Distributions in Empirical Finance: A Selected Survey," Working Papers 0904, University of Waterloo, Department of Economics, revised Sep 2009.
    4. Michael Rockinger & Maria Semenova, 2005. "Estimation of Jump-Diffusion Process vis Empirical Characteristic Function," FAME Research Paper Series rp150, International Center for Financial Asset Management and Engineering.
    5. Marine Carrasco & Jean-Pierre Florens, 2000. "Efficient GMM Estimation Using the Empirical Characteristic Function," Working Papers 2000-33, Center for Research in Economics and Statistics.
    6. Dinghai Xu & John Knight, 2011. "Continuous Empirical Characteristic Function Estimation of Mixtures of Normal Parameters," Econometric Reviews, Taylor & Francis Journals, vol. 30(1), pages 25-50.
    7. Robert J. Elliott & Carlton-James U. Osakwe, 2006. "Option Pricing for Pure Jump Processes with Markov Switching Compensators," Finance and Stochastics, Springer, vol. 10(2), pages 250-275, April.
    8. Tsionas, Efthymios G., 2012. "Maximum likelihood estimation of stochastic frontier models by the Fourier transform," Journal of Econometrics, Elsevier, vol. 170(1), pages 234-248.
    9. Dinghai Xu, 2009. "An Efficient Estimation for Switching Regression Models: A Monte Carlo Study," Working Papers 0903, University of Waterloo, Department of Economics, revised Apr 2009.
    10. Klar, Bernhard & Meintanis, Simos G., 2005. "Tests for normal mixtures based on the empirical characteristic function," Computational Statistics & Data Analysis, Elsevier, vol. 49(1), pages 227-242, April.

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