Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/107834
Authors: 
McAleer, Michael
Year of Publication: 
2014
Series/Report no.: 
Tinbergen Institute Discussion Paper 14-125/III
Abstract: 
The three most popular univariate conditional volatility models are the generalized autoregressive conditional heteroskedasticity (GARCH) model of Engle (1982) and Bollerslev (1986), the GJR (or threshold GARCH) model of Glosten, Jagannathan and Runkle (1992), and the exponential GARCH (or EGARCH) model of Nelson (1990, 1991). The underlying stochastic specification to obtain GARCH was demonstrated by Tsay (1987), and that of EGARCH was shown recently in McAleer and Hafner (2014). These models are important in estimating and forecasting volatility, as well as capturing asymmetry, which is the different effects on conditional volatility of positive and negative effects of equal magnitude, and leverage, which is the negative correlation between returns shocks and subsequent shocks to volatility. As there seems to be some confusion in the literature between asymmetry and leverage, as well as which asymmetric models are purported to be able to capture leverage, the purpose of the paper is two-fold, namely: (1) to derive the GJR model from a random coefficient autoregressive process, with appropriate regularity conditions; and (2) to show that leverage is not possible in these univariate conditional volatility models.
Subjects: 
Conditional volatility models
random coefficient autoregressive processes
random coefficient complex nonlinear moving average process
asymmetry
leverage
JEL: 
C22
C52
C58
G32
Document Type: 
Working Paper

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