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Erscheinungsjahr: 
2015
Schriftenreihe/Nr.: 
Tinbergen Institute Discussion Paper No. 15-022/III
Verlag: 
Tinbergen Institute, Amsterdam and Rotterdam
Zusammenfassung: 
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, such as EGARCH(1,0) or EGARCH(1,1), and possibly only under simulation. A limitation in the development of asymptotic properties of the QMLE for the EGARCH(p,q) model is the lack of an invertibility condition for the returns shocks underlying the model. It is shown in this paper that the EGARCH(p,q) 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(p,q) parameters.
Schlagwörter: 
Leverage
asymmetry
existence
stochastic process
asymptotic properties
invertibility
JEL: 
C22
C52
C58
G32
Dokumentart: 
Working Paper
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