The Research Of The Exponential Mixture Transition Distribution (EMTD) Model

In the daily life, analyzing the time-series data set is a problem which we often must face to. So the quality of the models affect the prediction of the future and the description of these datasets directly. We need different models to simulate different time-series datasets according to the characters which they exhibit. In this paper, we introduce the exponential mixture transition distribution model to study the non-Gaussian and nonlinear features of time series. This model is introduced from Le's(1996) GMTD model and based on mixture exponential distribution. The first-order and second-order stationary are derived. The genetic algorithm is used for estimation and some simulations are done which is different from the EM algorithm. Also we derive the standard error of the parameters and the (1 — α)% predicted region.The number of the mixture model's component is also a important research field. For this problem we adopt a distance which is based on optimization to determine the components and give some derivation.In order to explain the model and algorithm in this paper, we adopt some different methods to compare each other. The comparison is based on the one-step predicted region and one-step predicted value, also we give the derivation and use SAS software to obtain all the results. In this paper we also derive Le's model from one dimension to multiple dimensions, and use genetic algorithm to estimate the parameters.