Jump Point Detection And Curve Estimation For Discontinuous Time-Varying Coefficient Model

As a member of the non-parametric regression model,the time-varying coefficient model has attracted the attention of many researchers in recent years because of its adaptability and flexibility.However,most of the existing research on this model focuses on the premise that the coefficient function is smooth,which will make the estimator lack of asymptotic properties at the discontinuity point and its neighborhood,leading to large estimation errors.In fact,the time-varying sequence is likely to have discontinuities,and the appearance of these points is often accompanied by the occurrence of major events.At present,the research on the time-varying coefficient model with jumping points is very poor.Among them,there are shortcomings such as insufficient recognition of jumping points,complicated estimation process,difficult parameter selection,and large amount of calculation.In response to these problems,in this paper,on the basis of local polynomial regression,combined with the zero-crossing property of the second-order derivative function of the sequence with jumping points,a method for detecting and estimating the jumping points of time-varying coefficients(Time-varying coefficient Jump Point Detection and Fitness,abbreviated as TJPDF).The method first uses local polynomial regression to initially fit the time-varying coefficient function,expounds the parameter selection method of the time-varying coefficient model,and then identifies the outlier points in the first-order difference sequence of the initial estimate as the detected candidate jump points.After deleting the boundary area and the pseudo-hop points that are close to each other,the least root mean square error is used to determine the final jump point set,and finally the jump point set is estimated in segments.In numerical simulation,the TJPDF method can more accurately identify the location and number of jump points.Compared with the estimation method that does not consider the jump point,this method has no difference in the effect of the smooth segment,and has a smaller average integral square error in the jump point and the jump point neighborhood.In the case study,GDP and fixed asset investment of China are decomposed by the EEMD model and then reconstructed,and the TJPDF model is used to detect jump points on different frequency scales for the two.It is found that there are no jump points in the time-varying relationship between low-frequency sequences,while there are two jump points in the time-varying relationship between mid-frequency sequences in the fourth quarter of 2001 and the fourth quarter of 2008.Combined with the analysis of economic background,these two The occurrence of a jumping point at a time point is reasonable.Compared with not considering the jumping point,TJPDF has a better estimation effect.