Functional Coefficient Autoregression Models With Heavy Tailed

Functional Coefficient Autoregression Models (FAR models) is an importent model in nonlinear time series, but the study about this model at present is mostly supposedthatε_t is Gauss distribution. However,many evidences show that the heavy tail characteristic of distributions exist generally in many fields, such as economy, finances,traffic,hydrology and meteorology. That is to say, lots of data are heavy distribution,not Gauss distribution. Therefore, we propose the functional-coefficient autoregressive model with heavy tailed in this paper.where the function {a_j(.)} are measurable functions from R to R, and u is a dimensional random variable, u = X_t-i, (i = 1, ...,p), {ε_t} is a sequence of iid random variables andε_t is independent of {x_s, s < t}.In this article, the distribution ofε_t have following heavy probability :forα> 0, where L(x) is slowly varying at∞and x > 0,For above model, we study some probabilitic properties of this proposed model, and draw a conclusion, that is corollary 3.1.3. Next, we estimate the parameters of the proposed model using the local linear method, and discuss coincide properies and asymptotic properies of the estimation. The second conclusion is achieved, that is theoroem 3.2.2. Then we carry on the Moto Carlo simulation to the proposed model in this paper. By the simulation, we verified again that it is dependable to use local linear mothod estimate the proposed model. At last, we made empirial analysis basing on Shanghai stock index data. The computed result indicated that the proposed model is useful for the financial time series.