Mixture AR-GARCH Models And Mixture Nonlinear GARCH Models

Mixture time series, as an important kind of nonlinear time series models, has been proposed in recent years. The models can better describe the phenomenon of multimodal and fat tail. Compared with other nonlinear time series models, this one has the main advantage of offering a flexible and effective way to approximate any distribution form and building time series models easily. For some complicated distribution form that cannot be exactly described by probability distribution race with a single parameter, the mixture distribution models can infinitely approximate it.In the paper, on the basis of others'research findings, we mainly study the mixture autoregressive generally autoregressive conditional hetescedasticity model and a new nonlinear GARCH model which be extended to the mixture form. We obtain some results as follows:First, in the chapter 3, discussing the mixture autoregressive conditional hetescedasticity model and the mixture generally autoregressive conditional hetescedasticity model, we obtain the mixture autoregressive generally autoregressive conditional hetescedasticity model, to model nonlinear time series. The extended mixture model generalize the advantages of the former two mixture models that can better describe the phenomenon of multimodal and fat tail and have more less parameters estimated. The stationary conditions and the existed condition of the high moments of the mixture autoregressive generally autoregressive conditional hetescedasticity models has been discussed.Second, in the chapter 4, a new nonlinear GARCH model has been studied and extended to a mixture form. The sufficient stationary conditions of the mixture nonlinear GARCH model have been obtained by the theory of the Markov chains. The existed condition of the high moments of the model is explained.