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Journal of Financial Econometrics Vol. 2, No. 2, pp. 319-342
© 2004 Oxford University Press; all rights reserved.

Persistence and Kurtosis in GARCH and Stochastic Volatility Models

M. Angeles Carnero
     Universidad de Alicante

Daniel Peña
     Universidad Carlos III de Madrid

Esther Ruiz
     Universidad Carlos III de Madrid

Address correspondence to Esther Ruiz, Dpt. Estadística, Universidad Carlos III de Madrid, C/ Madrid 126, 28903 Getafe (Spain), or e-mail: ortega{at}est-econ.uc3m.es.

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.

KEYWORDS: ARSV, EGARCH, leverage effect, QGARCH

Received June 5, 2003; revised November 19, 2003; accepted November 24, 2003


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