Some Research About The MARMA Model And The HMTD Model

Mixture time series models ,as an important kind of nolinear time series models ,has been proposed in recent years.It has absorbed more and more attention. In this paper, we mainly study the mixture autoregressive moving average model and the heteroscedastic mixture transition distribution model.We obtain some results as follows:In chapter 2, a new mixture autoregressive moving average model is proposed for modeling nonlinear time series. The stationary conditions and autocorrelation function are derived. The EM algorithm for estimation of this model is given and shown to work well. The shape-changing feature of conditional distributions of the Mixture ARMA models makes these models capable of modeling time series with multimodal conditional distributions and with heteroscedasticity. To illustrate the usefulness of the models,we use the models and other competing models to some real datasets. The Mixture ARMA models appear to capture features of the real dataset better than other competing models do.In chapter 3, We mainly discuss the stationarity of the heteroscedastic mixture transition distribution model.Time series usually exhibit non-Gaussian features such as heteroscedasticity or suddern bursts of activity.To model such features,Berchtold generalized several models previously proposed to the heteroscedastic mixture transition distribution model.