Based On Functional Data Change Point Problem Research On Nonparametric Detection Methods

Since the 1970 s,the term change point has become a hot topic in academia.A large amount of literature has been accumulated for the problem of changing points of known data and distribution types.However,for data with unknown distribution,the parameter method is no longer applicable.The non-parameter method does not make any assumptions about the function form,thus increasing the selectivity and adaptability of the model.In the process of fitting the function using the observation data,It is more fully embodies the characteristics of allowing data to speak.Because the spline function method has better smoothness,stronger adaptability and more convenient calculation,therefore,this paper will use the spline function method to study the variation point and curve fitting problem of nonparametric regression model.In this thesis,we mainly consider the change point detection and curve fitting problem of nonparametric regression model in functional data,and analyze the functional relationship between response variable and independent variable.Based on the nonparametric regression model,the B-spline function and the smooth spline function are used to construct the non-parametric change point test statistic,and the central limit theory is used to analyze the asymptotic properties of the test statistic.Finally,the process of change point detection and curve fitting is given,The process of using R language combined with the method proposed in the paper,and a large number of numerical simulation related results are given.Finally,the theory of this paper is applied to the stock adjustment of Amazon stock and Tesla.The empirical analysis is carried out on the closing price index,and the major financial events corresponding to the change point are given in combination with the actual background,including but not limited to the internal structural adjustment of the enterprise.