Confidence Bands In The Semi-parametric Time Swries Regression

Partially linear models are extended linear regression models where one component is nonparametric. We consider the partially linear regression model with het-eroscedastic errors based on time series data. At the beginning of this paper, we introduce the background of kernel function and time series. The estimations of the parametric component, nonparametric component and variance function are provided in this paper. Furthermore, simultaneous confidence bands about the nonparametric part and variance function are obtained. And the coverage probabilities of the confidence bands are shown to be asymptotically correct. By the confidence bands, the problems of hypothesis testing in this model can be solved effectively. Simulation studies are carried out to evaluate the performance of the proposed method.