Article2002

NECESSARY AND SUFFICIENT MOMENT CONDITIONS FOR THE GARCH(r,s) AND ASYMMETRIC POWER GARCH(r,s) MODELS

288 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

Although econometricians have been using Bollerslev's (1986, Journal of Econometrics 31, 307–327) GARCH(r, s) model for over a decade, the higher order moment structure of the model remains unresolved. The sufficient condition for the existence of the higher order moments of the GARCH(r, s) model was given by Ling (1999a, Journal of Applied Probability 36, 688–705). This paper shows that Ling's condition is also necessary. As an extension, the necessary and sufficient moment conditions are established for Ding, Granger, and Engle's (1993, Journal of Empirical Finance, 1, 83–106) asymmetric power GARCH(r, s) model.

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References

1986Generalized autoregressive conditional heteroskedasticity 1982Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation 1992ARCH modeling in finance 2007Modelling Financial Time Series 2010A Long Memory Property of Stock Market Returns and a New Model 1992Stationarity of Garch processes and of some nonnegative time series 1992A Class of Nonlinear Arch Models

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