Template-Type: ReDIF-Paper 1.0
Series: Tinbergen Institute Discussion Papers
Creation-Date: 2014-06-16
Number: 14-069/III
Author-Name: Michael McAleer
Author-Workplace-Name: National Tsing Hua University, Taiwan, Erasmus University Rotterdam, the Netherlands, Complutense University of Madrid, Spain
Author-Name: Christian M. Hafner
Author-Workplace-Name: Université Catholique de Louvain, Belgium
Title: A One Line Derivation of EGARCH
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, there are as yet no statistical properties available for the (quasi-)maximum likelihood estimator of the EGARCH parameters. It is often argued heuristically that the reason for the lack of 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 or the derivation of statistical properties. It is shown in this paper that: (i) the EGARCH model can be derived from a random coefficient complex nonlinear moving average (RCCNMA) process; and (ii) the reason for the lack of statistical properties of the estimators of EGARCH is that the stationarity and invertibility conditions for the RCCNMA process are not known.
Classification-JEL: C22, C52, C58, G32
Keywords: Leverage, asymmetry, existence, random coefficient models, complex nonlinear moving average process
File-Url: https://papers.tinbergen.nl/14069.pdf
File-Format: application/pdf
File-Size: 88908 bytes
Handle: RePEc:tin:wpaper:20140069