Detecting Change In Persistence In Long Memory Time Series Via Df Ratio Statistic

The persistent change point is widely found in many time series data such as finance.In the literature,many scholars consider the detecting change in persistence between the unit root process and the short memory process.However,in real life,the persistent change point can also be easily found in the long memory time series.In this thesis,we focus on the detecting of one type persistent change point which changes from the unit root process to the long memory process.The main contents of the thesis are as follows:First of all,we propose a residual based DF ratio statistic to test persistent change point that changes from the unit root to long memory process with deterministic time trend.The limit distribution of the test statistic under the null hypothesis is proved,and with the help of the fractional order differential Sieve Bootstrap method,the critical value of the statistic is approximated.And the empirical sizes,powers of the test statistics obtained by numerical simulation,in addition,the test method have been practically applied in the exchange rate data with persistent change points.All results suggest that,this method can more effectively solve the problem studied in this thesis than the existing test methods,and the test method will not fail even when the model is extended to a(,)model or a heavy-tailed long memory time series model with a definite time trend.Secondly,the thesis considers the problem of testing change in persistence when the time series with the change parameters of the trend term changes from the unit root process to the long memory process.Through research,it is found that for the DF ratio method based on the estimated residuals of the entire sample,when there is a change point in the trend term,the persistent change point of the unit root process to a long memory process cannot be effectively tested,or in other words,as the position of the change point of the trend term parameter is later,the power is lower.To this end,it is proposed to first estimate the trend term parameters in stages,and then adopt the DF ratio statistics to test the persistent change point.The limit distribution of the test statistic under the null hypothesis was obtained by proof,and the critical value of the DF ratio statistic was asymptotically adopted by the fractional order differential Sieve Bootstrap method.The numerical simulation results and the analysis results of real exchange rate data show that the improved test method is effective and robust to the persistent change point test problem under consideration.Finally,in a time series with deterministic time trend,the online monitoring problem of persistent change point that changes from the unit root to long memory process.A monitoring statistic based on DF difference form is constructed,and the limit distribution of the monitoring statistic is given.Through numerical simulation,it is suggested that the fractional order differential Sieve Bootstrap method can effectively approximate the critical value of the statistics,the obtained empirical powers and average running lengths both illustrate the effectiveness of the monitoring method.In addition,the monitoring method still has a good monitoring effect when applied to heavy-tailed long memory time series with deterministic time trend.Furthermore,the practicality and reliability of this monitoring method are further demonstrated through the analysis of examples.