A One Line Derivation of EGARCH
By Michael Mcaleer, Christian M. Hafner. 2014
82 citations recorded by the source corpus.
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.
Subfields: Economics and Econometrics, Finance
View Paper: https://www.semanticscholar.org/paper/4b4c48e4b9eb28092c68afbfb867d1e8ced01f2a
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In Economics and Econometrics
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In Finance
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Citations in the corpus
- GARCH Modelling of Cryptocurrencies (2017, methodology): “A one line derivation of the EGARCH (1, 1) is described in McAleer and Hafner (2014).”
- Asymmetry and Leverage in Conditional Volatility Models (2014, unknown): “McAleer and Hafner (2014) showed that EGARCH could be derived from a random coefficient complex nonlinear moving average (RCCNMA) process, as follows: tttttt ηηψηφε ++= −− 11 || (6) where tφ ~ iid ),0( α , tψ ~ iid ),0( γ , tη ~ iid ),0( ω , 1−tη is a complex-valued function of 1−tη .”