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Normal Log-normal Mixture: Leptokurtosis, Skewness and Applications


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  • Minxian Yang


The properties and applications of the normal log-normal (NLN) mixture are considered. The moment of the NLN mixture is shown to be finite for any positive order. The expectations of exponential functions of a NLN mixture variable are also investigated. The kurtosis and skewness of the NLN mixture are explicitly shown to be determined by the variance of the log-normal and the correlation between the normal and log-normal. The issue of testing the NLN mixture is discussed. The NLN mixture is fitted to a set of cross-sectional data and a set of time-series data to demonstrate its applications. In the time series application, the ARCH-M effect and leverage effect are separately estimated and both appear to be supported by the data

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Bibliographic Info

Paper provided by Econometric Society in its series Econometric Society 2004 Australasian Meetings with number 186.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:ausm04:186

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Keywords: GARCH; stochastic volatility; ARCH-M; maximum likelihood;

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