Article1999

FOURTH MOMENT STRUCTURE OF THE GARCH( p , q ) PROCESS

133 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, a necessary and sufficient condition for the existence of the unconditional fourth moment of the GARCH( p , q ) process is given and also an expression for the moment itself. Furthermore, the autocorrelation function of the centered and squared observations of this process is derived. The statistical theory is further illustrated by a few special cases such as the GARCH(2,2) process and the ARCH( q ) process.

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References

1993ARCH MODELS: PROPERTIES, ESTIMATION AND TESTING 1996Statistical aspects of ARCH and stochastic volatility 1992Inequality Constraints in the Univariate GARCH Model 1999ARCH Models and Financial Applications 19967 GARCH models of volatility 1985The moment structure of ARCH processes

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