Monitoring Parameter Changes In Time Series Models

Some unexpected events in the financial market,such as the change of the government and the sudden financial crisis,will change the structure of the observation sequence,that is,change points occur.The online monitoring of financial time series can find the change point in time,and it is of great significance to adjust decisions and reduce financial risks.In this paper,we study the problem of monitoring change points in linear regression models and AR(p)models respectively.The research contents of the paper are as follows:Firstly,the on-line monitoring problem of parameter change points in linear model based on effective score vector is studied.The monitoring statistic is constructed and the limit property of the detector under the null hypothesis and the alternative hypothesis are proved.The empirical level,the empirical power and the average running length of the detector are given by Monte Carlo simulation method.And it is applied to the monitoring problem of stock price variance change point,which shows the effectiveness of the method.Secondly,the on-line monitoring problem of parameter change point in AR(p)model based on Range test is studied.Based on the effective score vector,Range detector is constructed and the limit property of the detector under the null hypothesis and the alternative hypothesis are proved.The empirical level,the empirical power and the average running length of the detector are given by Monte Carlo simulation method.And it is applied to the monitoring problem of stock price variance change point,which shows the effectiveness of the method.Finally,the on-line monitoring problem of parameter change point in AR(p)model based on CUSUM of residuals is studied.CUSUM of residuals monitoring statistic of the parameter change points is constructed,and the limit properties of the monitoring statistic are obtained under the null hypothesis and the alternative hypothesis.The Monte Carlo method is used to give the empirical level and empirical power of the monitoring statistic,and the effectiveness of the method is explained.