The Nonparametric Regression Model Of Variance Changing Point Estimates

The change point problem in time series analysis is a statistical study of a class of popular research direction, has attracted much attention of many scholars at home and abroad. Study on the change point before mainly focus on the changes of the mean, variance change point of the research now is in the hot period, this paper mainly uses non parametric method of time series variance change point of two cases were studied.This paper first introduces the background and significance of the research on change points, and nonparametric regression with parametric regression advantage. In addition based on the change point of existing theories and methods, the use of non parameter method of two kinds of time series variance change point are studied.The first one is to study the difference of independent random variables to unilaterally change point: according to the sequence of mean change point of independent thought, local law shows a good test effect of estimation, this paper based on the sliding window method and the combination of the variance change point problems are a sequence of independent random variables with local thought method, and gives the test statistic and the change point estimation of change point, and the distribution of limit test statistics, theory proves that this difference of change point estimator under the strong consistency and convergence rate, and the effectiveness of this method is verified by the numerical simulation.The second scenario is based on nonparametric regression model under random design variance change point: the use of local linear kernel estimation to fit the regression curve, and the structure of the residual sequence and the CUSUM test statistics, under certain assumptions derived the asymptotic distribution of the test statistic is proved, to verify the test statistic converges to the supremum of the Brown bridge, and the use of different kernel function estimation to verify the local linear kernel estimation for selection of kernel function is not affected, the numerical simulations verify the local linear kernel estimation than the other side of the kernel estimation problem is weakened, so as to improve and development of the original method.Finally we make a summary of this paper, and put forward the problems needed to be further studied.