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Properties and Estimation of Asymmetric Exponential Power Distribution

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  • ZHU, Dongming
  • ZINDE-WALSH, Victoria

Abstract

The new distribution class, Asymmetric Exponential Power Distribution (AEPD), proposed in this paper generalizes the class of Skewed Exponential Power Distributions (SEPD) in a way that in addition to skewness introduces different decay rates of density in the left and right tails. Our parametrization provides an interpretable role for each parameter. We derive moments and moment-based measures: skewness, kurtosis, expected shortfall. It is demonstrated that a maximum entropy property holds for the AEPD distributions. We establish consistency, asymptotic normality and efficiency of the maximum likelihood estimators over a large part of the parameter space by dealing with the problems created by non-smooth likelihood function and derive explicit analytical expressions of the asymptotic covariance matrix; where the results apply to the SEPD class they enlarge on the current literature. Finally, we give a convenient stochastic representation of the distribution; our Monte Carlo study illustrates the theoretical results.

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Bibliographic Info

Paper provided by Centre interuniversitaire de recherche en économie quantitative, CIREQ in its series Cahiers de recherche with number 13-2007.

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Length: 40 pages
Date of creation: 2007
Date of revision:
Handle: RePEc:mtl:montec:13-2007

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Keywords: asymmetric distributions; maximum likelihood estimation;

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References

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  1. Engle, Robert F & Ng, Victor K, 1993. " Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-78, December.
  2. Bawa, Vijay S., 1975. "Optimal rules for ordering uncertain prospects," Journal of Financial Economics, Elsevier, vol. 2(1), pages 95-121, March.
  3. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
  4. ZHU, Dongming & ZINDE-WALSH, Victoria, 2007. "Properties and Estimation of Asymmetric Exponential Power Distribution," Cahiers de recherche 13-2007, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  5. Mittnik, Stefan & Paolella, Marc S., 2003. "Prediction of Financial Downside-Risk with Heavy-Tailed Conditional Distributions," CFS Working Paper Series 2003/04, Center for Financial Studies (CFS).
  6. 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.
  7. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
  8. Hsieh, David A, 1989. "Modeling Heteroscedasticity in Daily Foreign-Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(3), pages 307-17, July.
  9. Torben G. Andersen & Tim Bollerslev & Peter F. Christoffersen & Francis X. Diebold, 2005. "Volatility Forecasting," PIER Working Paper Archive 05-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  10. Bickel, David R., 2002. "Robust estimators of the mode and skewness of continuous data," Computational Statistics & Data Analysis, Elsevier, vol. 39(2), pages 153-163, April.
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Cited by:
  1. Genaro Sucarrat & Alvaro Escribano, 2010. "The power log-GARCH model," Economics Working Papers we1013, Universidad Carlos III, Departamento de Economía.
  2. Victoria Zinde-Walsh & Dongming Zhu, 2007. "Properties And Estimation Of Asymmetric Exponential Power Distribution," Departmental Working Papers 2007-11, McGill University, Department of Economics.
  3. Asquith, William H., 2014. "Parameter estimation for the 4-parameter Asymmetric Exponential Power distribution by the method of L-moments using R," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 955-970.
  4. Zhu, Dongming & Galbraith, John W., 2011. "Modeling and forecasting expected shortfall with the generalized asymmetric Student-t and asymmetric exponential power distributions," Journal of Empirical Finance, Elsevier, vol. 18(4), pages 765-778, September.
  5. Harvey, A. & Sucarrat, G., 2012. "EGARCH models with fat tails, skewness and leverage," Cambridge Working Papers in Economics 1236, Faculty of Economics, University of Cambridge.
  6. M. Caivano & A. Harvey, 2013. "Time series models with an EGB2 conditional distribution," Cambridge Working Papers in Economics 1325, Faculty of Economics, University of Cambridge.
  7. Nadarajah, Saralees & Chan, Stephen & Afuecheta, Emmanuel, 2013. "On the characteristic function for asymmetric Student t distributions," Economics Letters, Elsevier, vol. 121(2), pages 271-274.

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