Research On Change Point Monitoring Of Two Kinds Of Regression Models

In the application of time series analysis,the study of the change point problem has theoretical value and practical application significance.For the study of the change point problem,the on-line monitoring method of the change point can continuously monitor the data and predict the moment when the change point occurs,so it has attracted the attention of many scholars.In this paper,the autoregressive model and the random coefficient autoregressive model are monitored online.Since the monitoring time has an important influence on the monitoring effect in the change point monitoring,it is generally expected that the average running time is as short as possible.If the monitoring time is shortened,it has important research significance.Therefore,this paper introduces window width parameters in these two regression models to adjust the monitoring start time,in order to shorten the average running time and achieve better monitoring results.For the online monitoring problem of the parameter change point of the autoregressive model,the window width parameter is introduced in the test statistic,the residual accumulation and the monitoring statistic of the parameter change point are constructed by the least squares method,and the starting time is adjusted,and the change point appears.The other moments move to the starting moment,improve the inspection potential,and shorten the average running length.It also proves the limit property of the monitoring statistic after introducing the window width parameter under the null hypothesis and alternative hypothesis.Finally,the effectiveness of the method is demonstrated by data simulation results.Aiming at the mean change point monitoring problem of the random coefficient autoregressive time series model,a window width parameter is introduced in the monitoring statistics and boundary function,and the monitoring statistics are constructed to adjust the monitoring start time,and the consistent estimator of the inserted parameters is estimated.The parameters are replaced,giving the limit distribution of the monitoring statistics under the null hypothesis and alternative hypotheses.The posterior test of the model is given to ensure the stability of the historical sample data.Finally,the limit theory and the simulation calculation of the posterior test are given,and the effectiveness of the method is illustrated.