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Continuous Empirical Characteristic Function Estimation of Mixtures of Normal Parameters

Author

Listed:
  • Dinghai Xu

    (Department of Economics, University of Waterloo)

  • John Knight

    (Department of Economics, University of Western Ontario)

Abstract

This paper develops an e±cient method for estimating the discrete mix- tures of normal family based on the continuous empirical characteristic function (CECF). An iterated estimation procedure based on the closed form objective distance function is proposed to improve the estimation effciency. The results from the Monte Carlo simulation reveal that the CECF estimator produces good finite sample properties. In particular, it outperforms the discrete type of methods when the maximum likelihood estimation fails to converge. An empirical example is provided for illustrative purposes.

Suggested Citation

  • Dinghai Xu & John Knight, 2008. "Continuous Empirical Characteristic Function Estimation of Mixtures of Normal Parameters," Working Papers 08006, University of Waterloo, Department of Economics.
    • Handle: RePEc:wat:wpaper:08006
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    File URL: http://economics.uwaterloo.ca/documents/Xu-MNviaCECF.pdf
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    References listed on IDEAS

    as
    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. Knight, John L. & Yu, Jun, 2002. "Empirical Characteristic Function In Time Series Estimation," Econometric Theory, Cambridge University Press, vol. 18(3), pages 691-721, June.
    3. 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.
    4. Kien Tran, 1998. "Estimating mixtures of normal distributions via empirical characteristic function," Econometric Reviews, Taylor & Francis Journals, vol. 17(2), pages 167-183.
    5. French, Kenneth R., 1980. "Stock returns and the weekend effect," Journal of Financial Economics, Elsevier, vol. 8(1), pages 55-69, March.
    6. 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.
    7. G. J. McLachlan, 1987. "On Bootstrapping the Likelihood Ratio Test Statistic for the Number of Components in a Normal Mixture," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(3), pages 318-324, November.
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    Citations

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    Cited by:

    1. Cornelis J. Potgieter & Marc G. Genton, 2013. "Characteristic Function-based Semiparametric Inference for Skew-symmetric Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(3), pages 471-490, September.
    2. Hodoshima, Jiro & Yamawake, Toshiyuki, 2019. "Comparison of utility indifference pricing and mean-variance approach under a normal mixture distribution with time-varying volatility," Finance Research Letters, Elsevier, vol. 28(C), pages 74-81.
    3. Dinghai Xu & John Knight, 2013. "Stochastic volatility model under a discrete mixture-of-normal specification," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 37(2), pages 216-239, April.
    4. 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.

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    More about this item

    Keywords

    Empirical characteristic function; Mixtures of normal.;

    JEL classification:

    • 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
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions

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