The Limit Properties Of Nonparametric Change-Point Estimation In Variance

The change-point problem is always an important research direction in mathemat-ical statistics,and it has a wide range of applications in the fields of finance,economics,meteorology and genetics.Variance describes the degree of dispersion and volatility of data,nowadays the research on change-points in variance has attracted more and more attention.Based on the non-parametric variance change-point model,this paper pro-poses a sum of power weighted cumulative sum estimation of change-point in variance,and proves the consistency of the variance change-point estimation method,and gives the convergence rate and asymptotic distribution,and constructs the asymptotic con-fidence interval.Sum of power weighted cumulative sum estimation is also given,and the limit properties of the method are also proved.Then we compare the estimation ac-curacy of these two methods and cumulative sum(CUSUM)estimations with different parameters with computer simulation under different distributions and change-point po-sition.Finally,a real data case of the volatility change-point of the SSE 50ETF option is given,which shows the application of these methods in practical problems.