On the Invertibility of EGARCH

Type of content
Discussion / Working Papers
Publisher's DOI/URI
Thesis discipline
Degree name
Publisher
University of Canterbury. Department of Economics and Finance
Journal Title
Journal ISSN
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Language
Date
2014
Authors
Martinet, G.G.
McAleer, M.
Abstract

Of the two most widely estimated univariate asymmetric conditional volatility models, the exponential GARCH (or EGARCH) specification can capture asymmetry, which refers to the different effects on conditional volatility of positive and negative effects of equal magnitude, and leverage, which refers to the negative correlation between the returns shocks and subsequent shocks to volatility. However, the statistical properties of the (quasi-) maximum likelihood estimator (QMLE) of the EGARCH parameters are not available under general conditions, but only for special cases under highly restrictive and unverifiable conditions. A limitation in the development of asymptotic properties of the QMLE for EGARCH is the lack of an invertibility condition for the returns shocks underlying the model. It is shown in this paper that the EGARCH model can be derived from a stochastic process, for which the invertibility conditions can be stated simply and explicitly. This will be useful in re-interpreting the existing properties of the QMLE of the EGARCH parameters.

Description
Citation
Martinet, G. G., McAleer, M., (2014) On the Invertibility of EGARCH. 12pp..
Keywords
Leverage, asymmetry, existence, stochastic process, asymptotic properties, invertibility
Ngā upoko tukutuku/Māori subject headings
ANZSRC fields of research
Fields of Research::38 - Economics::3802 - Econometrics::380202 - Econometric and statistical methods
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