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dc.contributor.authorDe Jongh, P.J.
dc.contributor.authorVenter, J.H.
dc.identifier.citationDe Jongh, P.J. & Venter, J.H. 2015. A framework for normal mean variance mixture innovations with application to Garth modelling. South African statistical journal, 49(2):139-152. []en_US
dc.identifier.issn1996-8450 (Online)
dc.description.abstractGARCH models are useful to estimate the volatility of financial return series. Historically the innovation distribution of a GARCH model was assumed to be standard normal but recent research emphasizes the need for more general distributions allowing both asymmetry (skewness) and kurtosis in the innovation distribution to obtain better fitting models. A number of authors have proposed models which are special cases of the class of normal mean variance mixtures. We introduce a general framework within which this class of innovation distributions may be discussed. This entails writing the innovation term as a standardised combination of two variables, namely a normally distributed term and a mixing variable, each with its own interpretation. We list the existing models that fit into this framework and compare the corresponding innovation distributions, finding that they tend to be quite similar. This is confirmed by an empirical illustration which fits the models to the monthly excess returns series of the US stocks. The illustration finds further support for the ICAPM model of Merton, thus supporting recent results of Lanne and Saikonnen (2006)en_US
dc.description.sponsorshipNational Research Foundation and by industry (Absa and SAS Institute).en_US
dc.subjectGARCH modelsen_US
dc.subjectnormal gammaen_US
dc.subjectnormal inverse gammaen_US
dc.subjectnormal inverse Gaussianen_US
dc.subjectnormal log-normalen_US
dc.subjectnormal mean variance mixturesen_US
dc.subjectz distributionen_US
dc.titleA framework for normal mean variance mixture innovations with application to Garth modellingen_US
dc.contributor.researchID11749318 - De Jongh, Pieter Juriaan
dc.contributor.researchID10168907 - Venter, Johannes Hendrik

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