A One Line Derivation of EGARCH

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ID: 69918
2014
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Abstract
One of the most popular univariate asymmetric conditional volatility models is the exponential GARCH (or EGARCH) specification. In addition to asymmetry, which captures the different effects on conditional volatility of positive and negative effects of equal magnitude, EGARCH can also accommodate leverage, which is the negative correlation between returns shocks and subsequent shocks to volatility. However, the statistical properties of the (quasi-) maximum likelihood estimator of the EGARCH parameters are not available under general conditions, but rather only for special cases under highly restrictive and unverifiable conditions. It is often argued heuristically that the reason for the lack of general statistical properties arises from the presence in the model of an absolute value of a function of the parameters, which does not permit analytical derivatives, and hence does not permit (quasi-) maximum likelihood estimation. It is shown in this paper for the non-leverage case that: (1) the EGARCH model can be derived from a random coefficient complex nonlinear moving average (RCCNMA) process; and (2) the reason for the lack of statistical properties of the estimators of EGARCH under general conditions is that the stationarity and invertibility conditions for the RCCNMA process are not known.
Reference Key
mcaleer2014aeconometrics Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors McAleer, Michael;Hafner, Christian M.;
Journal econometrics
Year 2014
DOI
DOI not found
URL
http://www.mdpi.com/2225-1146/2/2/92
Keywords
Biology (General) Information technology environmental effects of industries and plants renewable energy sources environmental sciences economics as a science agriculture finance social sciences economic theory. demography energy industries. energy policy. fuel trade probabilities. mathematical statistics

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