Moving Ratio Test For Multiple Changes In Long Memory Time Series

Test methods which were designed for single change point problem usually invalid when detecting multiple change points.This thesis detects the mean,variance and long memory parameter multiple change points in long memory time series via a moving method.The validity of the proposed methods are verified by theoretical analysis,numerical simulation and actual data analysis.The main contents are as follows:First,we propose a moving ratio statistic to detect the mean change points in long memory time series.The null distribution of the test statistic as well as its consistency under the alternative hypothesis are proved.Simulations show that the proposed method can effectively solve the failure problem of single change point test method when detecting multiple change points.And the change point problems in a set of annual Nile flow data and a set of Northern hemisphere temperature data are analyzed.The next,a moving ratio statistic is proposed to test variance change points in long memory time series.The null distribution of the test statistic as well as its consistency under the alternative hypothesis are proved.Simulations indicate that the proposed method performs well when detecting multiple change points in variance.Further more,we illustrated our method in a group of Qinghai coal yield data.Once more proposes a moving ratio statistic to study the detecting problem of long memory parameter change points in stationary long memory process.The limit distribution of the test statistic under the stationary long memory process null hypothesis is given.The numerical simulations show that the moving ratio method can significantly improve the empirical power when detecting multiple change points.And the validity and feasibility of the proposed test method are illustrated through a group of American durable goods order data.In the end,we summarize the full text,and gives some prospects about multiple change points test problem in long memory time series.