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Persistence and Kurtosis in GARCH and Stochastic Volatility Models

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M. Angeles Carnero

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Abstract

This article shows that the relationship between kurtosis, persistence of shocks to volatility, and first-order autocorrelation of squares is different in GARCH and ARSV models. This difference can explain why, when these models are fitted to the same series, the persistence estimated is usually higher in GARCH than in ARSV models, and, why gaussian ARSV models seem to be adequate, whereas GARCH models often require leptokurtic conditional distributions. We also show that introducing the asymmetric response of volatility to positive and negative returns does not change the conclusions. These results are illustrated with the analysis of daily financial returns. Copyright 2004, Oxford University Press.

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File URL: http://hdl.handle.net/10.1093/jjfinec/nbh012
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Publisher Info
Article provided by Oxford University Press in its journal Journal of Financial Econometrics.

Volume (Year): 2 (2004)
Issue (Month): 2 ()
Pages: 319-342
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Handle: RePEc:oup:jfinec:v:2:y:2004:i:2:p:319-342

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  1. PREMINGER, Arie & HAFNER, Christian M., 2006. "Deciding between GARCH and stochastic volatility via strong decision rules," CORE Discussion Papers 2006042, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
  2. Christian Bauer, 2007. "A Better Asymmetric Model of Changing Volatility in Stock and Exchange Rate Returns: Trend-GARCH," European Journal of Finance, Taylor and Francis Journals, vol. 13(1), pages 65-87, January. [Downloadable!] (restricted)
  3. Michael McAleer & Marcelo Cunha Medeiros, 2006. "Realized volatility: a review," Textos para discussão 531 Publication status: F, Department of Economics PUC-Rio (Brazil). [Downloadable!]
    Other versions:
  4. 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. [Downloadable!]
  5. 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. [Downloadable!]
  6. Peter Winker & Manfred Gilli & Vahidin Jeleskovic, 2007. "An objective function for simulation based inference on exchange rate data," Journal of Economic Interaction and Coordination, Springer, vol. 2(2), pages 125-145, December. [Downloadable!] (restricted)
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  7. Oleg Korenok & Stanislav Radchenko, 2005. "The smooth transition autoregressive target zone model with the Gaussian stochastic volatility and TGARCH error terms with applications," Econometrics 0508015, EconWPA. [Downloadable!]
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  8. Teräsvirta, Timo, 2006. "An introduction to univariate GARCH models," Working Paper Series in Economics and Finance 646, Stockholm School of Economics. [Downloadable!]
  9. Hafner, Christian M. & Manner, Hans, 2008. "Dynamic stochastic copula models: Estimation, inference and applications," Research Memoranda 043, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
  10. Alberto Mora-Galan & Ana Perez & Esther Ruiz, 2004. "Stochastic Volatility Models And The Taylor Effect," Statistics and Econometrics Working Papers ws046315, Universidad Carlos III, Departamento de Estadística y Econometría. [Downloadable!]
  11. Esther Ruiz & Helena Veiga, 2006. "Modelling Long-Memory Volatilities With Leverage Effect: Almsv Versus Fiegarch," Statistics and Econometrics Working Papers ws066016, Universidad Carlos III, Departamento de Estadística y Econometría. [Downloadable!]
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