On the Invertibility of EGARCH

Guillaume Gaetan Martinet and Michael McAleer
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Guillaume Gaetan Martinet: Paris Tech, France; Columbia University, United States

No 14-096/III, Tinbergen Institute Discussion Papers from Tinbergen Institute

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.

Keywords: Leverage; asymmetry; existence; stochastic process; asymptotic properties; invertibility (search for similar items in EconPapers)
JEL-codes: C22 C52 C58 G32 (search for similar items in EconPapers)
Date: 2014-07-25
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Related works:
Journal Article: On the invertibility of EGARCH(p, q) (2018)
Working Paper: On the Invertibility of EGARCH(p,q) (2015)
Working Paper: On the Invertibility of EGARCH(p,q) (2015)
Working Paper: On the Invertibility of EGARCH(p,q) (2015)
Working Paper: On the Invertibility of EGARCH (2014)
Working Paper: On the Invertibility of EGARCH (2014)
Working Paper: On the Invertibility of EGARCH (2014)
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