Journal of Financial Econometrics Vol. 2, No. 2, pp. 211-250
© 2004 Oxford University Press; all rights reserved.
Mixed Normal Conditional Heteroskedasticity
University of Munich
University of Munich, Center for Financial Studies, and Ifo Institute for Economic Research
University of Zurich
Address correspondence to Stefan Mittnik, Chair of Financial Econometrics, Institute of Statistics, University of Munich, D-80799 Munich, Germany, or e-mail: finmetrics{at}stat.uni-muenchen.de.
Both unconditional mixed normal distributions and GARCH models with fat-tailed conditional distributions have been employed in the literature for modeling financial data. We consider a mixed normal distribution coupled with a GARCH-type structure (termed MN-GARCH) which allows for conditional variance in each of the components as well as dynamic feedback between the components. Special cases and relationships with previously proposed specifications are discussed and stationarity conditions are derived. For the empirically most relevant GARCH(1,1) case, the conditions for existence of arbitrary integer moments are given and analytic expressions of the unconditional skewness, kurtosis, and autocorrelations of the squared process are derived. Finally, employing daily return data on the NASDAQ index, we provide a detailed empirical analysis and compare both the in-sample fit and out-of-sample forecasting performance of the MN-GARCH as well as recently proposed Markov-switching models. We show that the MN-GARCH approach can generate a plausible disaggregation of the conditional variance process in which the components' volatility dynamics have a clearly distinct behavior, which is, for example, compatible with the well-known leverage effect.
KEYWORDS: GARCH, kurtosis, leverage effect, Markov-switching, skewness, stationarity, value-at-risk
Received September 23, 2002; revised December 19, 2003; accepted January 24, 2004
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