Statistical Inference Of Persistent Change Points Of Long Memory Sequences With Non-constant Variance

With the continuous development of long memory time series theory,the use of long memory time series to characterize the evolution characteristics of economic and financial data has been widely used.In view of whether the sequence is stationary or not,it determines a completely different time series modeling method.It is important for improving the accuracy of the model to accurately determine whether the sequence exist persistence changes.The traditional persistence change test is based on the assumption that the sequence has the same variance,but the time series data tends to have heteroscedasticity,which will cause the relevant conclusions to no longer apply.Therefore,this paper introduces heteroscedasticity based on the long-term memory time series persistence change test,and considers the influence of heteroscedasticity on long-term memory time series persistence change test and estimation.The persistence change problem is studied based on the cumulative sum method.When the variance is constant,the generalized central limit theorem is used to prove that the limit distribution under the null hypothesis is the functional of fractional Brownian motion.When the variance is non-constant,the limit distribution no longer depends only on the long memory index,but also on the jump amplitude,direction of change and moment of change of the variance change point.When the alternative hypothesis is established,the value of the test potential function of the statistic has different degrees of loss.In particular,when the persistent change point changes from stationary sequence to non-stationary sequence,the variance change in a negative direction,the jump amplitude increases and the change point is later,the loss phenomenon is more serious.At the same time,the persistent change point estimation problem is considered in six different situations.The results show that the accuracy of the estimation is still affected by the variance change point.For the persistence change test and the estimation of the defects affected by the heteroscedasticity,the Bootstrap method is used to reduce the interference effect of the and effectiveness of the proposed method are proved by using two sets of financial time series data.