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Exact Maximum Likelihood estimation for the BL-GARCH model under elliptical distributed innovations

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In this paper, we discuss the class of Bilinear GATRCH (BL-GARCH) models which are capable of capturing simultaneously two key properties of non-linear time series : volatility clustering and leverage effects. It has been observed often that the marginal distributions of such time series have heavy tails ; thus we examine the BL-GARCH model in a general setting under some non-Normal distributions. We investigate some probabilistic properties of this model and we propose and implement a maximum likelihood estimation (MLE) methodology. To evaluate the small-sample performance of this method for the various models, a Monte Carlo study is conducted. Finally, within-sample estimation properties are studied using S&P 500 daily returns, when the features of interest manifest as volatility clustering and leverage effects.

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  • Abdou Kâ Diongue & Dominique Guegan & Rodney C. Wolff, 2008. "Exact Maximum Likelihood estimation for the BL-GARCH model under elliptical distributed innovations," Documents de travail du Centre d'Economie de la Sorbonne b08027, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  • Handle: RePEc:mse:cesdoc:b08027
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    1. Zhang, Xiaobo & Kanbur, Ravi, 2005. "Spatial inequality in education and health care in China," China Economic Review, Elsevier, vol. 16(2), pages 189-204.
    2. C. Simon Fan & Oded Stark, 2008. "Looking At The "Population Problem" Through The Prism Of Heterogeneity: Welfare And Policy Analyses," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 49(3), pages 799-835, August.
    3. Blackorby,Charles & Bossert,Walter & Donaldson,David J., 2005. "Population Issues in Social Choice Theory, Welfare Economics, and Ethics," Cambridge Books, Cambridge University Press, number 9780521532587, December.
    4. Becker, Gary S & Lewis, H Gregg, 1973. "On the Interaction between the Quantity and Quality of Children," Journal of Political Economy, University of Chicago Press, vol. 81(2), pages 279-288, Part II, .
    5. Zhang, Jie & Zhang, Junsen, 2007. "Optimal social security in a dynastic model with investment externalities and endogenous fertility," Journal of Economic Dynamics and Control, Elsevier, vol. 31(11), pages 3545-3567, November.
    6. Sah, Raaj Kumar, 1991. "The Effects of Child Mortality Changes on Fertility Choice and Parental Welfare," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 582-606, June.
    7. Alessandro Balestrino & Alessandro Cigno & Anna Pettini, 2002. "Endogenous Fertility and the Design of Family Taxation," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 9(2), pages 175-193, March.
    8. Zhang, Jie, 2003. "Optimal debt, endogenous fertility, and human capital externalities in a model with altruistic bequests," Journal of Public Economics, Elsevier, vol. 87(7-8), pages 1825-1835, August.
    9. Cigno, Alessandro & Pettini, Anna, 2002. "Taxing family size and subsidizing child-specific commodities?," Journal of Public Economics, Elsevier, vol. 84(1), pages 75-90, April.
    10. Galor, Oded, 2005. "From Stagnation to Growth: Unified Growth Theory," Handbook of Economic Growth,in: Philippe Aghion & Steven Durlauf (ed.), Handbook of Economic Growth, edition 1, volume 1, chapter 4, pages 171-293 Elsevier.
    11. Galor, Oded & Weil, David N, 1996. "The Gender Gap, Fertility, and Growth," American Economic Review, American Economic Association, vol. 86(3), pages 374-387, June.
    12. Willis, Robert J, 1973. "A New Approach to the Economic Theory of Fertility Behavior," Journal of Political Economy, University of Chicago Press, vol. 81(2), pages 14-64, Part II, .
    13. Chakraborty, Shankha, 2004. "Endogenous lifetime and economic growth," Journal of Economic Theory, Elsevier, vol. 116(1), pages 119-137, May.
    14. Philippe Michel & Bertrand Wigniolle, 2007. "On Efficient Child Making," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 307-326.
    15. David N. Weil & Oded Galor, 1999. "From Malthusian Stagnation to Modern Growth," American Economic Review, American Economic Association, pages 150-154.
    16. Larry E. Jones & Alice Schoonbroodt, 2010. "Complements Versus Substitutes And Trends In Fertility Choice In Dynastic Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 51(3), pages 671-699, August.
    17. J. Ignacio Conde-Ruiz & Eduardo L. Giménez & Mikel Pérez-Nievas, 2010. "Millian Efficiency with Endogenous Fertility," Review of Economic Studies, Oxford University Press, pages 154-187.
    18. Nerlove, Marc & Razin, Assaf & Sadka, Efraim, 1986. "Some Welfare Theoretic Implications of Endogenous Fertility," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 27(1), pages 3-31, February.
    19. David de la Croix & Axel Gosseries, 2007. "Procreation, Migration and Tradable Quotas," Chapters,in: Population Aging, Intergenerational Transfers and the Macroeconomy, chapter 9 Edward Elgar Publishing.
    20. Nerlove, Marc & Raut, Lakshmi K., 1993. "Growth models with endogenous population: A general framework," Handbook of Population and Family Economics,in: M. R. Rosenzweig & Stark, O. (ed.), Handbook of Population and Family Economics, edition 1, volume 1, chapter 20, pages 1117-1174 Elsevier.
    21. Xiaobo Zhang & Kevin Honglin Zhang, 2002. "Regional Inequality," Chapters,in: The Globalization of the Chinese Economy, chapter 8 Edward Elgar Publishing.
    22. Spiegel, Y., 1993. "Rawlsian Optimal Population Size," Papers 97, Bell Communications - Economic Research Group.
    23. Eckstein, Zvi & Wolpin, Kenneth I., 1985. "Endogenous fertility and optimal population size," Journal of Public Economics, Elsevier, vol. 27(1), pages 93-106, June.
    24. Razin, Assaf & Ben-Zion, Uri, 1975. "An Intergenerational Model of Population Growth," American Economic Review, American Economic Association, vol. 65(5), pages 923-933, December.
    25. Loupias, C. & Wigniolle, B., 2000. "Regime de retraite et chute de la natalite : evolution des moeurs ou arbitrage micro-economique," Papiers d'Economie Mathématique et Applications 2000.95, Université Panthéon-Sorbonne (Paris 1).
    26. David de la Croix & Matthias Doepke, 2003. "Inequality and Growth: Why Differential Fertility Matters," American Economic Review, American Economic Association, vol. 93(4), pages 1091-1113, September.
    27. Gary S. Becker & Robert J. Barro, 1988. "A Reformulation of the Economic Theory of Fertility," The Quarterly Journal of Economics, Oxford University Press, pages 1-25.
    28. BAUDIN, Thomas, 2010. "The optimal trade-off between quality and quantity with uncertain child survival," CORE Discussion Papers 2010057, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    29. van Groezen, Bas & Leers, Theo & Meijdam, Lex, 2003. "Social security and endogenous fertility: pensions and child allowances as siamese twins," Journal of Public Economics, Elsevier, vol. 87(2), pages 233-251, February.
    30. Michael Bar & Oksana Leukhina, 2010. "Demographic Transition and Industrial Revolution: A Macroeconomic Investigation," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 13(2), pages 424-451, April.
    31. Spiegel, Yossef, 1993. "Rawlsian Optimal Population Size," Journal of Population Economics, Springer;European Society for Population Economics, vol. 6(4), pages 363-373, November.
    32. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
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    1. Motelle, Sephooko & Biekpe, Nicholas, 2015. "Financial integration and stability in the Southern African development community," Journal of Economics and Business, Elsevier, vol. 79(C), pages 100-117.

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    Keywords

    BL-GARCH process; elliptical distribution; leverage effects; maximum likelihood; Monte Carlo method; volatility clustering.;

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