IDEAS home Printed from https://ideas.repec.org/p/mcl/mclwop/2007-11.html
   My bibliography  Save this paper

Properties And Estimation Of Asymmetric Exponential Power Distribution

Author

Listed:
  • Victoria Zinde-Walsh
  • Dongming Zhu

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 di¤erent 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 e¢ ciency 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.

Suggested Citation

  • Victoria Zinde-Walsh & Dongming Zhu, 2007. "Properties And Estimation Of Asymmetric Exponential Power Distribution," Departmental Working Papers 2007-11, McGill University, Department of Economics.
    • Handle: RePEc:mcl:mclwop:2007-11
    as

    Download full text from publisher

    File URL: http://www.mcgill.ca/files/economics/propertiesandestimation.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    2. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2005. "Volatility forecasting," CFS Working Paper Series 2005/08, Center for Financial Studies (CFS).
    3. 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.
    4. 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.
    5. 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.
    6. 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 1749-1778, December.
    7. 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).
    8. Bawa, Vijay S., 1975. "Optimal rules for ordering uncertain prospects," Journal of Financial Economics, Elsevier, vol. 2(1), pages 95-121, March.
    9. Christoffersen, Peter, 2011. "Elements of Financial Risk Management," Elsevier Monographs, Elsevier, edition 2, number 9780123744487.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    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. Hu, Michael Y. & Jiang, Christine X. & Tsoukalas, Christos, 1997. "The European exchange rates before and after the establishment of the European Monetary System," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 7(3), pages 235-253, October.
    6. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, Department of Economics and Business Economics, Aarhus University.
    7. Xekalaki, Evdokia & Degiannakis, Stavros, 2005. "Evaluating volatility forecasts in option pricing in the context of a simulated options market," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 611-629, April.
    8. Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May.
    9. Bollerslev, Tim & Ghysels, Eric, 1996. "Periodic Autoregressive Conditional Heteroscedasticity," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(2), pages 139-151, April.
    10. Bronka Rzepkowski, 2001. "Pouvoir prédictif de la volatilité implicite dans le prix des options de change," Économie et Prévision, Programme National Persée, vol. 148(2), pages 71-97.
    11. Degiannakis, Stavros & Xekalaki, Evdokia, 2004. "Autoregressive Conditional Heteroskedasticity (ARCH) Models: A Review," MPRA Paper 80487, University Library of Munich, Germany.
    12. Vacca, Gianmarco & Zoia, Maria Grazia & Bagnato, Luca, 2022. "Forecasting in GARCH models with polynomially modified innovations," International Journal of Forecasting, Elsevier, vol. 38(1), pages 117-141.
    13. Eskandar A. Tooma, 2003. "Modeling and Forecasting Egyptian Stock Market Volatility Before and After Price Limits," Working Papers 0310, Economic Research Forum, revised Apr 2003.
    14. Perry Sadorsky & Michael D. McKenzie, 2008. "Power transformation models and volatility forecasting," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 27(7), pages 587-606.
    15. J. Miguel Marin & Genaro Sucarrat, 2015. "Financial density selection," The European Journal of Finance, Taylor & Francis Journals, vol. 21(13-14), pages 1195-1213, November.
    16. Alizadeh, Amir H. & Gabrielsen, Alexandros, 2013. "Dynamics of credit spread moments of European corporate bond indexes," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 3125-3144.
    17. Christofi, A. & Pericli, A., 1999. "Correlation in price changes and volatility of major Latin American stock markets," Journal of Multinational Financial Management, Elsevier, vol. 9(1), pages 79-93, January.
    18. Wang, Jianxin & Yang, Minxian, 2009. "Asymmetric volatility in the foreign exchange markets," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 19(4), pages 597-615, October.
    19. Renatas Kizys & Peter Spencer, 2007. "Assessing the Relation between Equity Risk Premium and Macroeconomic Volatilities in the UK," Discussion Papers 07/13, Department of Economics, University of York.
    20. Alagidede, Paul & Panagiotidis, Theodore, 2009. "Modelling stock returns in Africa's emerging equity markets," International Review of Financial Analysis, Elsevier, vol. 18(1-2), pages 1-11, March.

    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:mcl:mclwop:2007-11. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Shama Rangwala (email available below). General contact details of provider: https://edirc.repec.org/data/demcgca.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.