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Maximum Likelihood Estimation for the Asymmetric Exponential Power Distribution

Author

Listed:
  • Mahdi Teimouri

    (Gonbad Kavous University)

  • Saralees Nadarajah

    (University of Manchester)

Abstract

The asymmetric exponential power (AEP) distribution has received much attention in economics and finance. Simulation study shows that iterative methods developed for finding the maximum likelihood (ML) estimates of the AEP distribution sometimes fail to converge. In this paper, the expectation–maximization (EM) algorithm is proposed to find the ML estimates of the AEP distribution which always converges. Performance of the EM algorithm is demonstrated by simulations and a real data illustration. As an application, the proposed EM algorithm is applied to find the ML estimates for the regression coefficients when the error term in a linear regression model follows the AEP distribution. Performance of the AEP distribution in robust simple regression modelling is established through a real data illustration.

Suggested Citation

  • Mahdi Teimouri & Saralees Nadarajah, 2022. "Maximum Likelihood Estimation for the Asymmetric Exponential Power Distribution," Computational Economics, Springer;Society for Computational Economics, vol. 60(2), pages 665-692, August.
    • Handle: RePEc:kap:compec:v:60:y:2022:i:2:d:10.1007_s10614-021-10162-1
    DOI: 10.1007/s10614-021-10162-1
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    1. Panayiotis Theodossiou, 2015. "Skewed Generalized Error Distribution of Financial Assets and Option Pricing," Multinational Finance Journal, Multinational Finance Journal, vol. 19(4), pages 223-266, December.
    2. Zhu, Dongming & Galbraith, John W., 2010. "A generalized asymmetric Student-t distribution with application to financial econometrics," Journal of Econometrics, Elsevier, vol. 157(2), pages 297-305, August.
    3. Basso, Rodrigo M. & Lachos, Víctor H. & Cabral, Celso Rômulo Barbosa & Ghosh, Pulak, 2010. "Robust mixture modeling based on scale mixtures of skew-normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 2926-2941, December.
    4. Ivana Komunjer, 2007. "Asymmetric power distribution: Theory and applications to risk measurement," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(5), pages 891-921.
    5. Prates, Marcos Oliveira & Lachos, Victor Hugo & Barbosa Cabral, Celso Rômulo, 2013. "mixsmsn: Fitting Finite Mixture of Scale Mixture of Skew-Normal Distributions," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 54(i12).
    6. Nolan, John P. & Ojeda-Revah, Diana, 2013. "Linear and nonlinear regression with stable errors," Journal of Econometrics, Elsevier, vol. 172(2), pages 186-194.
    7. Christoffersen, Peter & Dorion, Christian & Jacobs, Kris & Wang, Yintian, 2010. "Volatility Components, Affine Restrictions, and Nonnormal Innovations," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(4), pages 483-502.
    8. Eugene F. Fama, 1963. "Mandelbrot and the Stable Paretian Hypothesis," The Journal of Business, University of Chicago Press, vol. 36, pages 420-420.
    9. DiCiccio T.J. & Monti A.C., 2004. "Inferential Aspects of the Skew Exponential Power Distribution," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 439-450, January.
    10. Nolan, John P., 1998. "Parameterizations and modes of stable distributions," Statistics & Probability Letters, Elsevier, vol. 38(2), pages 187-195, June.
    11. Zhu, Dongming & Zinde-Walsh, Victoria, 2009. "Properties and estimation of asymmetric exponential power distribution," Journal of Econometrics, Elsevier, vol. 148(1), pages 86-99, January.
    12. W. R. Gilks & P. Wild, 1992. "Adaptive Rejection Sampling for Gibbs Sampling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(2), pages 337-348, June.
    13. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    14. Butler, Richard J, et al, 1990. "Robust and Partially Adaptive Estimation of Regression Models," The Review of Economics and Statistics, MIT Press, vol. 72(2), pages 321-327, May.
    15. Hsieh, David A, 1989. "Modeling Heteroscedasticity in Daily Foreign-Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(3), pages 307-317, July.
    16. Karlis, Dimitris & Xekalaki, Evdokia, 2003. "Choosing initial values for the EM algorithm for finite mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 577-590, January.
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