A framework for normal mean variance mixture innovations with application to Garth modelling
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Date
Authors
De Jongh, P.J.
Venter, J.H.
Journal Title
Journal ISSN
Volume Title
Publisher
SASA
Abstract
GARCH 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)
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Citation
De 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. [http://reference.sabinet.co.za/webx/access/electronic_journals/sasj/sasj_v49_n2_a1.pdf]