A Study Of Several Types Of Change Point Problems For Linear Process Models

Change point problems exist in many fields,especially in economics,finance,industrial quality and other industries,so it is of great practical significance to study the change point problem.Linear process model is an important model in time series.The paper focus on the estimation of variance change points,mean change point detection and persistent change point detection of linear process model.For the estimation of the variance change point of the linear process,the cumulative sum(CUSUM)method is used to study the variance change point.Under the condition of the mean change is unchanged,the consistency of the variance change point estimation is proved,and their convergence rate is given.For the detection of the change point of the mean change of the heavy-tailed linear process sequence,the test statistic is given by the Ratio test method based on the CUSUM function,and at the same time,the asymptotic distribution of the test statistic under the null hypothesis and the asymptotic progression under the alternative conditions are given.For heavy-tailed series of linear processes,the Ratio statistic whose denominator is the cumulative sum of residual squares is used to truncate the persistent change point.After truncating,the asymptotic distribution of the statistics under the null hypothesis converges to the functional of the Wiener process,and it is independent of the heavy-tailed index.