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Revisiting Several Popular GARCH Models with Leverage Effect: Differences and Similarities

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  • María José Rodríguez
  • Esther Ruiz

Abstract

In this paper, we analyze five of the most popular models proposed to represent conditional heteroscedasticity with leverage effect, namely, GQARCH, TGARCH, GJR, EGARCH, and APARCH. We show that when the parameters satisfy the positivity, stationarity, and finite kurtosis conditions, the dynamics that the GJR and GQARCH models can represent are heavily limited while those of the TGARCH and EGARCH models are less restricted. Alternatively, when the parameters of the GQARCH and GJR models are estimated without restrictions, one can often conclude that the unconditional variance or kurtosis of returns do not exist even when they truly do. Copyright The Author, 2012. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org, Oxford University Press.

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  • María José Rodríguez & Esther Ruiz, 2012. "Revisiting Several Popular GARCH Models with Leverage Effect: Differences and Similarities," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 10(4), pages 637-668, September.
  • Handle: RePEc:oup:jfinec:v:10:y:2012:i:4:p:637-668
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    1. He, Changli & Ter svirta, Timo & Malmsten, Hans, 2002. "Moment Structure Of A Family Of First-Order Exponential Garch Models," Econometric Theory, Cambridge University Press, vol. 18(04), pages 868-885, August.
    2. Drost, Feike C & Nijman, Theo E, 1993. "Temporal Aggregation of GARCH Processes," Econometrica, Econometric Society, vol. 61(4), pages 909-927, July.
    3. Asger Lunde & Peter R. Hansen, 2005. "A forecast comparison of volatility models: does anything beat a GARCH(1,1)?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 873-889.
    4. Wu, Guojun & Xiao, Zhijie, 2002. "A generalized partially linear model of asymmetric volatility," Journal of Empirical Finance, Elsevier, vol. 9(3), pages 287-319, August.
    5. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    6. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    7. Robert Engle, 2004. "Risk and Volatility: Econometric Models and Financial Practice," American Economic Review, American Economic Association, vol. 94(3), pages 405-420, June.
    8. Jan G. De Gooijer & Kurt Brännäs, 2004. "Asymmetries in conditional mean and variance: modelling stock returns by asMA-asQGARCH," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(3), pages 155-171.
    9. Babsiri, Mohamed El & Zakoian, Jean-Michel, 2001. "Contemporaneous asymmetry in GARCH processes," Journal of Econometrics, Elsevier, vol. 101(2), pages 257-294, April.
    10. M. Karanasos & J. Kim, 2003. "Moments of the ARMA--EGARCH model," Econometrics Journal, Royal Economic Society, vol. 6(1), pages 146-166, June.
    11. Antonis Demos, 2002. "Moments and dynamic structure of a time-varying parameter stochastic volatility in mean model," Econometrics Journal, Royal Economic Society, vol. 5(2), pages 345-357, June.
    12. Meddahi, Nour & Renault, Eric, 2004. "Temporal aggregation of volatility models," Journal of Econometrics, Elsevier, vol. 119(2), pages 355-379, April.
    13. Harvey, Andrew C & Shephard, Neil, 1996. "Estimation of an Asymmetric Stochastic Volatility Model for Asset Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 429-434, October.
    14. Bollerslev, Tim & Russell, Jeffrey & Watson, Mark (ed.), 2010. "Volatility and Time Series Econometrics: Essays in Honor of Robert Engle," OUP Catalogue, Oxford University Press, number 9780199549498.
    15. Karanasos, Menelaos & Kim, Jinki, 2006. "A re-examination of the asymmetric power ARCH model," Journal of Empirical Finance, Elsevier, vol. 13(1), pages 113-128, January.
    16. Stelios Arvanitis & Antonis Demos, 2004. "Time Dependence and Moments of a Family of Time-Varying Parameter Garch in Mean Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(1), pages 1-25, January.
    17. Pan, Jiazhu & Wang, Hui & Tong, Howell, 2008. "Estimation and tests for power-transformed and threshold GARCH models," Journal of Econometrics, Elsevier, vol. 142(1), pages 352-378, January.
    18. Zhang, Xibin & King, Maxwell L., 2008. "Box-Cox stochastic volatility models with heavy-tails and correlated errors," Journal of Empirical Finance, Elsevier, vol. 15(3), pages 549-566, June.
    19. Yu, Jun, 2005. "On leverage in a stochastic volatility model," Journal of Econometrics, Elsevier, vol. 127(2), pages 165-178, August.
    20. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. " On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    21. Enrique Sentana, 1995. "Quadratic ARCH Models," Review of Economic Studies, Oxford University Press, vol. 62(4), pages 639-661.
    22. Ruiz, Esther & Veiga, Helena, 2008. "Modelling long-memory volatilities with leverage effect: A-LMSV versus FIEGARCH," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 2846-2862, February.
    23. 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.
    24. Balaban, Ercan, 2004. "Comparative forecasting performance of symmetric and asymmetric conditional volatility models of an exchange rate," Economics Letters, Elsevier, vol. 83(1), pages 99-105, April.
    25. Dima Alberg & Haim Shalit & Rami Yosef, 2008. "Estimating stock market volatility using asymmetric GARCH models," Applied Financial Economics, Taylor & Francis Journals, vol. 18(15), pages 1201-1208.
    26. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, June.
    27. Changli He & Annastiina Silvennoinen & Timo Teräsvirta, 2008. "Parameterizing Unconditional Skewness in Models for Financial Time Series," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 6(2), pages 208-230, Spring.
    28. Changli He & Timo Terasvirta & Hans Malmsten, 1999. "Fourth Moment Structure of a Family of First-Order Exponential GARCH Models," Research Paper Series 29, Quantitative Finance Research Centre, University of Technology, Sydney.
    29. So, Mike K P & Li, W K & Lam, K, 2002. "A Threshold Stochastic Volatility Model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 21(7), pages 473-500, November.
    30. Kawakatsu, Hiroyuki, 2007. "Specification and estimation of discrete time quadratic stochastic volatility models," Journal of Empirical Finance, Elsevier, vol. 14(3), pages 424-442, June.
    31. Chen, Cathy W.S. & Gerlach, Richard & So, Mike K.P., 2006. "Comparison of nonnested asymmetric heteroskedastic models," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2164-2178, December.
    32. He, Changli & Terasvirta, Timo, 1999. "Properties of moments of a family of GARCH processes," Journal of Econometrics, Elsevier, vol. 92(1), pages 173-192, September.
    33. M. Angeles Carnero, 2004. "Persistence and Kurtosis in GARCH and Stochastic Volatility Models," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(2), pages 319-342.
    34. Geoffrey F. Loudon & Wing H. Watt & Pradeep K. Yadav, 2000. "An empirical analysis of alternative parametric ARCH models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(2), pages 117-136.
    35. M. Angeles Carnero & Daniel Peña & Esther Ruiz, 2008. "Estimating and Forecasting GARCH Volatility in the Presence of Outiers," Working Papers. Serie AD 2008-13, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    36. Robert F. Engle, 2011. "Long-Term Skewness and Systemic Risk," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 9(3), pages 437-468, Summer.
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    Cited by:

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    3. M. Angeles Carnero & Ana Pérez & Esther Ruiz, 2016. "Identification of asymmetric conditional heteroscedasticity in the presence of outliers," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 7(1), pages 179-201, March.
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    5. Zhang, Dalu, 2014. "Vine copulas and applications to the European Union sovereign debt analysis," International Review of Financial Analysis, Elsevier, vol. 36(C), pages 46-56.
    6. André Lucas & Bernd Schwaab & Xin Zhang, 2017. "Modeling Financial Sector Joint Tail Risk in the Euro Area," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(1), pages 171-191, January.
    7. Linton, Oliver & Whang, Yoon-Jae & Yen, Yu-Min, 2016. "A nonparametric test of a strong leverage hypothesis," Journal of Econometrics, Elsevier, vol. 194(1), pages 153-186.
    8. repec:taf:oaefxx:v:5:y:2017:i:1:p:1318812 is not listed on IDEAS
    9. M. Angeles Carnero Fernández & Ana Pérez Espartero, 2018. "Outliers and misleading leverage effect in asymmetric GARCH-type models," Working Papers. Serie AD 2018-01, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    10. Haas, Markus & Krause, Jochen & Paolella, Marc S. & Steude, Sven C., 2013. "Time-varying mixture GARCH models and asymmetric volatility," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 602-623.
    11. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.
    12. El Euch Omar & Fukasawa Masaaki & Rosenbaum Mathieu, 2016. "The microstructural foundations of leverage effect and rough volatility," Papers 1609.05177, arXiv.org.
    13. Pradosh Simlai, 2012. "Endogenous Information, Risk Characterization, and the Predictability of Average Stock Returns," Brazilian Review of Finance, Brazilian Society of Finance, vol. 10(3), pages 291-315.

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