The Research For Variance Change In Non-parametric Regression Model Under Two Different Statistics

The change-point analysis in financial time series has been regarded as one of the core areas of research in statistics. Recently, numerous studies related to this problem have been appear. This paper studies the problem of testing and estimation of change-point in non-parametric regression models and obtain several results as follows:In chapter1, we consider the introduction of background knowledge of non-parametric regression models.In chapter2, we consider the problem of testing for a variance change point in non-parametric time series regression models both under fixed and random design cases. In this part, we propose a CUSUM of squares test statistics to detect the variance change. Based on the square of residual, it is show that under certain conditions, the distribution of test statistics under null hypothesis is proved to be the function of a standard Brownian. A number of simulation examples and real data analysis have been done to support the validity of the CUSUM models in this chapter.In chapter3, we consider the problem of testing for a variance change point in non-parametric time series regression models with AR(P) both under fixed and random design cases. In this part, we propose a Ratio test statistics to detect the variance change. Based on the Ratio test of residual, it is show that under certain conditions, the distribution of test statistics under null hypothesis is proved to be the function of a standard Brownian. A number of simulation examples and real data analysis have been done to support the validity of the Ratio models in this chapter.In chapter4, The outlook and summary of the non-parametric model.