Statistical Inferences For Change Points Of The Long Memory Indexes

Since the 1980 s,the long memory time sequence theory has been developed rapidly in the field of econometrics and has been widely used in the research areas of economy and finance.At the same time,the problem of detecting breaks is also highly valued by economists.Nowadays,more and more financial data which show characteristics of long memory series,and structural changes often appear in the financial time series.In view of this,it is very important to study the problem of detecting changes of long memory sequence indexes.The innovation of this article is as follows.Firstly,a long memory series regression model with breaks in indexes has been established,testing for changes in indexes of series based on the ratio test statistic.The study found that,under the null hypothesis,the ratio test statistic converges to a Fractional Brown Bridge,and under the alternative hypothesis,the ratio test statistic is divergent.The data simulation results show that,the rejection rate increases with the increase of the sample size,which is close to 5% under the null hypothesis,under the alternative hypothesis,the rejection rate increases along with the increase of sample size and the increase of the index jump range,the highest value reached 66.3%.In addition,the estimation of the change points depend on the different long memory time series and the sample size,more precisely,the estimated value of the changes will be more accurate and close to the real value with the increase of the index jump range.The Monte Carlo simulation shows that the theory is in agreement with the experimental simulation.Secondly,a long memory sequence regression model with changes in mean and indexes has been established,detecting change points in indexes of series based on the ratio test statistic.The study found that,under the null hypothesis,the ratio test statistic is divergent at the rate of021 dT-,under the alternative hypothesis,the ratio test statistic tends to infinity.The data simulation results show that,under the null hypothesis,the rejection rate increases with the increase of the mean jump amplitude,and decreases with the increase of the long memory indexes,the mean plays a decisive role,which may lead to overestimating the long memoryindexes,and even lead to misjudgment of the researchers,under the alternative hypothesis,the rejection rate increases with the increase of the mean jump and the increase of the index jump range,and which tends to infinity,and the influence of the mean is relatively large.The Monte Carlo simulation is to verify the rationality and legitimacy of the theory.In conclusion,two long memory regression models above can use the ratio test statistic to effectively detect breaks in the long memory indexes,similarly,numerical simulation can verify the rationality and legitimacy of the theory.