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Maximum entropy autoregressive conditional heteroskedasticity model

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  • Park, Sung Y.
  • Bera, Anil K.
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    Abstract

    In many applications, it has been found that the autoregressive conditional heteroskedasticity (ARCH) model under the conditional normal or Student's t distributions are not general enough to account for the excess kurtosis in the data. Moreover, asymmetry in the financial data is rarely modeled in a systematic way. In this paper, we suggest a general density function based on the maximum entropy (ME) approach that takes account of asymmetry, excess kurtosis and also of high peakedness. The ME principle is based on the efficient use of available information, and as is well known, many of the standard family of distributions can be derived from the ME approach. We demonstrate how we can extract information functional from the data in the form of moment functions. We also propose a test procedure for selecting appropriate moment functions. Our procedure is illustrated with an application to the NYSE stock returns. The empirical results reveal that the ME approach with a fewer moment functions leads to a model that captures the stylized facts quite effectively.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Econometrics.

    Volume (Year): 150 (2009)
    Issue (Month): 2 (June)
    Pages: 219-230

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    Handle: RePEc:eee:econom:v:150:y:2009:i:2:p:219-230

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    Web page: http://www.elsevier.com/locate/jeconom

    Related research

    Keywords: Maximum entropy density ARCH models Excess kurtosis Asymmetry Peakedness of distribution Stock returns data;

    References

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    1. Lee, Sang-Won & Hansen, Bruce E., 1994. "Asymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator," Econometric Theory, Cambridge University Press, vol. 10(01), pages 29-52, March.
    2. Chen, Yi-Ting & Chou, Ray Y. & Kuan, Chung-Ming, 2000. "Testing time reversibility without moment restrictions," Journal of Econometrics, Elsevier, vol. 95(1), pages 199-218, March.
    3. Li, David X & Turtle, H J, 2000. "Semiparametric ARCH Models: An Estimating Function Approach," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(2), pages 174-86, April.
    4. Yuichi Kitamura & Michael Stutzer, 1997. "An Information-Theoretic Alternative to Generalized Method of Moments Estimation," Econometrica, Econometric Society, vol. 65(4), pages 861-874, July.
    5. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, vol. 19(02), pages 280-310, April.
    6. Zellner, Arnold & Highfield, Richard A., 1988. "Calculation of maximum entropy distributions and approximation of marginalposterior distributions," Journal of Econometrics, Elsevier, vol. 37(2), pages 195-209, February.
    7. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    8. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
    9. Wang, Kai-Li & Fawson, Christopher B. & Barrett, Christopher B. & McDonald, James B., 1998. "A Flexible Parametric Garch Model With An Application To Exchange Rates," Economics Research Institute, ERI Study Papers 28355, Utah State University, Economics Department.
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    11. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-50, July.
    12. Engle, Robert F & Gonzalez-Rivera, Gloria, 1991. "Semiparametric ARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(4), pages 345-59, October.
    13. Dhaene, Geert & Hoorelbeke, Dirk, 2004. "The information matrix test with bootstrap-based covariance matrix estimation," Economics Letters, Elsevier, vol. 82(3), pages 341-347, March.
    14. Ryu, Hang K., 1993. "Maximum entropy estimation of density and regression functions," Journal of Econometrics, Elsevier, vol. 56(3), pages 397-440, April.
    15. McDonald, James B. & Newey, Whitney K., 1988. "Partially Adaptive Estimation of Regression Models via the Generalized T Distribution," Econometric Theory, Cambridge University Press, vol. 4(03), pages 428-457, December.
    16. Golan, Amos & Judge, George G. & Miller, Douglas, 1996. "Maximum Entropy Econometrics," Staff General Research Papers 1488, Iowa State University, Department of Economics.
    17. Gallant, A. Ronald, 1981. "On the bias in flexible functional forms and an essentially unbiased form : The fourier flexible form," Journal of Econometrics, Elsevier, vol. 15(2), pages 211-245, February.
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    Cited by:
    1. Vilkkumaa, Eeva & Liesiö, Juuso & Salo, Ahti, 2014. "Optimal strategies for selecting project portfolios using uncertain value estimates," European Journal of Operational Research, Elsevier, vol. 233(3), pages 772-783.
    2. Namaki, A. & Koohi Lai, Z. & Jafari, G.R. & Raei, R. & Tehrani, R., 2013. "Comparing emerging and mature markets during times of crises: A non-extensive statistical approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(14), pages 3039-3044.
    3. Bera, A. K. & Galvao Jr, A. F. & Montes-Rojas, G. & Park, S. Y., 2010. "Which quantile is the most informative? Maximum likelihood, maximum entropy and quantile regression," Working Papers 10/08, Department of Economics, City University London.
    4. Usta, Ilhan & Kantar, Yeliz Mert, 2011. "On the performance of the flexible maximum entropy distributions within partially adaptive estimation," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2172-2182, June.

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