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Moment Structure Of A Family Of First-Order Exponential Garch Models

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  • He, Changli
  • Ter svirta, Timo
  • Malmsten, Hans
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    Abstract

    In this paper we consider the moment structure of a class of first-order exponential generalized autoregressive conditional heteroskedasticity (GARCH) models. This class contains as special cases both the standard exponential GARCH model and the symmetric and asymmetric logarithmic GARCH model. Conditions for the existence of any arbitrary moment are given. Furthermore, the expressions for the kurtosis and the autocorrelations of positive powers of absolute-valued observations are derived. The properties of the autocorrelation structure are discussed and compared to those of the standard first-order GARCH process. In particular, it is seen that, contrary to the standard GARCH case, the decay rate of the autocorrelations of squared errors is not constant and that the rate can be quite rapid in the beginning, depending on the parameters of the model.

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    Bibliographic Info

    Article provided by Cambridge University Press in its journal Econometric Theory.

    Volume (Year): 18 (2002)
    Issue (Month): 04 (August)
    Pages: 868-885

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    Handle: RePEc:cup:etheor:v:18:y:2002:i:04:p:868-885_18

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    Cited by:
    1. Francq, Christian & Wintenberger, Olivier & Zakoïan, Jean-Michel, 2013. "GARCH models without positivity constraints: Exponential or log GARCH?," Journal of Econometrics, Elsevier, vol. 177(1), pages 34-46.
    2. Pérez, Ana & Ruiz, Esther & Veiga, Helena, 2009. "A note on the properties of power-transformed returns in long-memory stochastic volatility models with leverage effect," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3593-3600, August.
    3. Wintenberger, Olivier, 2013. "Continuous invertibility and stable QML estimation of the EGARCH(1,1) model," MPRA Paper 46027, University Library of Munich, Germany.
    4. Fernandes, Marcelo & Grammig, Joachim, 2002. "A Family of Autoregressive Conditional Duration Models," Economics Working Papers (Ensaios Economicos da EPGE) 440, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
    5. repec:imd:wpaper:wp2010-25 is not listed on IDEAS
    6. Jérôme Vandenbussche & Stanley Watt & Szabolcs Blazsek, 2009. "The Liquidity and Liquidity Distribution Effects in Emerging Markets," IMF Working Papers 09/228, International Monetary Fund.
    7. Malmsten, Hans & Teräsvirta, Timo, 2004. "Stylized Facts of Financial Time Series and Three Popular Models of Volatility," Working Paper Series in Economics and Finance 563, Stockholm School of Economics, revised 03 Sep 2004.
    8. María José Rodríguez & Esther Ruiz, 2009. "GARCH models with leverage effect : differences and similarities," Statistics and Econometrics Working Papers ws090302, Universidad Carlos III, Departamento de Estadística y Econometría.
    9. Malmsten, Hans, 2004. "Evaluating exponential GARCH models," Working Paper Series in Economics and Finance 564, Stockholm School of Economics, revised 03 Sep 2004.
    10. Christian M. Dahl & Emma M. Iglesias, 2008. "The limiting properties of the QMLE in a general class of asymmetric volatility models," CREATES Research Papers 2008-38, School of Economics and Management, University of Aarhus.
    11. 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.
    12. Liudas Giraitis & Remigijus Leipus & Peter M. Robinson & Donatas Surgailis, 2004. "LARCH, leverage, and long memory," LSE Research Online Documents on Economics 294, London School of Economics and Political Science, LSE Library.
    13. Hartz, Christoph & Mittnik, Stefan & Paolella, Marc, 2006. "Accurate value-at-risk forecasting based on the normal-GARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2295-2312, December.
    14. Sofia Anyfantaki & Antonis Demos, 2012. "Estimation and Properties of a Time-Varying EGARCH(1,1) in Mean Model," DEOS Working Papers 1228, Athens University of Economics and Business.
    15. Liudas Giraitis & Remigijus Leipus & Peter M Robinson & Donatas Surgailis, 2003. "LARCH, Leverage and Long Memory," STICERD - Econometrics Paper Series /2003/460, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    16. Genaro Sucarrat & Alvaro Escribano, 2010. "The power log-GARCH model," Economics Working Papers we1013, Universidad Carlos III, Departamento de Economía.
    17. 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.
    18. Wintenberger, Olivier & Cai, Sixiang, 2011. "Parametric inference and forecasting in continuously invertible volatility models," MPRA Paper 31767, University Library of Munich, Germany.

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