Estimation Of Change Point In Linear Process

Change point problem is in many fields,particularly in the areas of economics,finance,and quality control,so it is important to research the estimation of change points.Unfor-tunately,in most papers,the estimator of the change performs poorly in the case when the change point occurred at the early position and the end position of the sequence.In this paper,we propose a method,which can be achieved by discarding a part of observations,to improve the precision of the CUSUM estimator,and we also give the relevant theoretical analysis.Chapter 1,we introduce the research trends at home and abroad about the change point problem.Then we elaborate the background and main work of this paper.Chapter 2,We use the CUSUM type estimator to estimate the variance change and do theoretical analysis about the error probability of the bias of the CUSUM estimator.The precision is effected by the location of the variance change and the variances of the split sequences before and behind the change date.When the change occurs in early stage of the sequence where the variance of before is bigger the behind and the change happens in late stage of the sequence where the variance of before is smaller the behind,the estimation is poor.Due to this,the iterative truncation method is proposed and the method moves the possible change date to another relative date where the upper bound of the probability of the absolute bias of the CUSUM estimation gets smaller.Monte Carlo simulations demonstrate that the improvement of the proposed method is nontrivial.As an example,the variance change the SSE Composite Index returns is located precisely.Chapter 3,We use the CUSUM type estimator to estimate the mean change and analysis the error probability of the bias of the CUSUM estimator.The precision is effected by the location of the mean change and the means jump before and behind the change date.Similarly,we give the iterative truncation method to locate the change in the mean.Monte Carlo simulations demonstrate that the improvement of the proposed method is effective.As an example,the mean change of the stock closing price returns of leshi is given.The 4th chapter is the conclusion which summarizes the paper,generalizes the whole thesis and points out the significance and the research contents of the method proposed in this paper in the future.