Accurate Estimation Of The Mean Variability Of Long Memory Time Series

It is of great practical significance to test and estimate possible change points in time series.Different from the traditional methods of testing and estimating change points based on statistical inference,the method of accurately estimating the number and position of change points from the point of view of model optimization is a new hot spot of statistical research in recent years.However,the previous studies mainly focus on short memory time series models.In this paper,we study the accurate estimation of mean change points in long memory time series models.The main contents are as follows:First,by numerical simulation,the likelihood ratio scanning method has many advantages in the accurate estimation of the change point in the piecewise stationary auto-regression model,but there are many shortcomings when it is used to estimate the mean change point in the long memory time series directly,for example,with the increase of long memory parameters,the frequency of correctly estimating the number of change points decrease significantly,and the deviation of the change points location estimation increases.In this paper,a new scanning method based on the difference of fractional order and the re-construction of the likelihood ratio statistic based on the difference sequence is proposed.The simulation results show that the new method is better than the original method in estimating the mean change point in the long memory time series.The feasibility and practicability of the new likelihood ratio scanning method is realized by a set of daily return data of Shanghai Stock Exchange Index.Secondly,in order to solve the problem that the estimation accuracy of the likelihood ratio scanning method rapidly deteriorates with the decrease of the heavy tail index when estimating the change point in heavy-tail time series,the rank likelihood ratio scanning method suitable for the heavy-tail auto-regressive sequence and the heavy-tail long memory time series is proposed respectively.The basic idea of the rank likelihood ratio scanning method is to first rank the data and then re-construct the likelihood ratio statistic with the rank instead of the original data.Through the numerical simulation,it is found that the proposed rank likelihood ratio scanningmethod can improve the estimation precision greatly,and the influence of the size of the heavy tail index on the estimation accuracy is very small.And the like.Finally,the feasibility and practicability of the rank likelihood ratio scanning method are illustrated by analyzing the change points in a group of daily return data of Shenzhen index.