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Normal Log-normal Mixture: Leptokurtosis, Skewness and Applications


  • 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

Suggested Citation

  • Minxian Yang, 2004. "Normal Log-normal Mixture: Leptokurtosis, Skewness and Applications," Econometric Society 2004 Australasian Meetings 186, Econometric Society.
  • Handle: RePEc:ecm:ausm04:186

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    Cited by:

    1. Thilo A. Schmitt & Rudi Schafer & Holger Dette & Thomas Guhr, 2015. "Quantile Correlations: Uncovering temporal dependencies in financial time series," Papers 1507.04990,
    2. Stephane Hess & John Rose, 2012. "Can scale and coefficient heterogeneity be separated in random coefficients models?," Transportation, Springer, vol. 39(6), pages 1225-1239, November.
    3. Thilo A. Schmitt & Rudi Schäfer & Holger Dette & Thomas Guhr, 2015. "Quantile Correlations: Uncovering Temporal Dependencies In Financial Time Series," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(07), pages 1-16, November.

    More about this item


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

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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