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Abstract

Through considering the volatility asymmetry in financial markets, we extend the threshold autoregressive conditional heteroskedasticity model to the general threshold autoregressive conditional heteroskedasticity model with asymmetry. The sufficient conditions for the existence of the stationary solution and the finiteness of the moments of the model are derived. The parameters and the threshold value of the model are estimated using the quasi-maximum likelihood method. The results of Monte Carlo simulation method show that the method performs well. By applying this method to the Shanghai daily return and volatility series with the significant leverage effect, we find that the asymmetric model with general threshold better reflects the asymmetric fluctuation characteristics than the original model.

Keywords

Volatility asymmetry GARCH model threshold value maximum likelihood method Monte Carlo simulation

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A general threshold GARCH process with volatility asymmetry

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