Article2002

MOMENT STRUCTURE OF A FAMILY OF FIRST-ORDER EXPONENTIAL GARCH MODELS

Changli He · Timo Teräsvirta Y · Hans Malmsten

103 citations0/0 files storedEconometric Theory

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Financial Risk and Volatility Modeling Stochastic processes and financial applications Complex Systems and Time Series Analysis

Abstract

In this paper we consider the moment structure of a class of first-order exponential generalized autoregressive conditional heteroskedasticity (GARCH) models. This class contains as special cases both the standard exponential GARCH model and the symmetric and asymmetric logarithmic GARCH model. Conditions for the existence of any arbitrary moment are given. Furthermore, the expressions for the kurtosis and the autocorrelations of positive powers of absolute-valued observations are derived. The properties of the autocorrelation structure are discussed and compared to those of the standard first-order GARCH process. In particular, it is seen that, contrary to the standard GARCH case, the decay rate of the autocorrelations of squared errors is not constant and that the rate can be quite rapid in the beginning, depending on the parameters of the model.

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References

1986Generalized autoregressive conditional heteroskedasticity 1991Conditional Heteroskedasticity in Asset Returns: A New Approach 1993Measuring and Testing the Impact of News on Volatility 1993A long memory property of stock market returns and a new model 19965 Stochastic volatility 1995All in the family Nesting symmetric and asymmetric GARCH models 1998The detection and estimation of long memory in stochastic volatility 2002MIXING AND MOMENT PROPERTIES OF VARIOUS GARCH AND STOCHASTIC VOLATILITY MODELS

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