Mean Change And Unit Root Test With Long Memory Series

The problem of change point has been a hot issue in the financial and econometric fields at home and abroad.Since 1980,long memory sequences have been widely used in life,such as environmental science,medical hygiene,hydrogeography,statistics,finance,and economics.On the other hand,there are more and more non-stationary data appearing in financial data,and more and more data obey long memory time series distribution.Based on the above background,this paper studies the long memory sequence model with variance change points,and focuses on the unit root test and the mean change point test.The specific research content is as follows:First,when studying the long-memory sequence unit root test with variance point,the central limit theorem with variance change point is constructed,and the limit distribution of statistics is obtained.The theoretical proof shows that the test statistic is convergent.Data experimental results show that the factors affect the unit root test mainly include long memory index,variance jump attitude,sample size,and variance change position.Under the null hypothesis,the size increases with the increase of sample size and variance jump attitude,and decreases with the increase of long memory index.Under the alternative hypothesis,the effect is more obvious under the larger samples of small samples.As the jump attitude of the variance points increases,the power gradually decreases;in addition,as the long memory index increases,the power gradually decline.Second,the variance point of the long memory sequence containing the mean change point was tested.Based on the central limit theorem given in the article,the limit distribution of statistics under the null hypothesis is obtained,and it is concluded that the statistics are convergent.The numerical simulation results show that under the null hypothesis,the size increases as the mean jump attitude increases;in addition,as the long memory index increases,the size gradually decreases;finally,with the sample size increase,the size gradually increases.Under the alternative hypothesis,the test statistic is divergent.Experimental results show that the higher of the variance change point is,the higher of the power is.Secondly,when the variance jump attitude is less than 1,the power decreases as the variance jump attitude increases;variance jump attitude is less than 1,the power decreases as the variance jump attitude increases;when the variance jump attitude is greater than 1,We can draw the opposite conclusion.Finally,the research results obtained in this paper are a good supplement and perfection to the theory of the test of variance points under the long memory sequence.It has a certain theoretical significance,and has certain application value in the field of stock analysis.