Abstract: Aiming at the modeling problem of Z-valued time series data with volatility, we proposed a Z-valued Taylor-Schwert generalized autoregressive conditional heteroscedasticity model based on Poisson distribution. Firstly, some statistical properties of the model were derived. Secondly, the unknown parameters in the model were estimated by using the condition maximum likelihood estimation method, and the asymptotic properties of estimators were proved. Thirdly, numerical simulations were conducted to demonstrate the  performance of the estimation method. Finally, a real daily stock return data was considered, and the superiority of the proposed model over existing models was proved through analysis of the fitting results of the data.

Key words: Z-valued time series, GARCH model, condition maximum likelihood estimation, heteroscedasticity