The Online Monitoring Research On Change Point Of Regression Models

The main research of this paper is the problem of online monitoring point in theregression models, first we according to the time series build the regression models and usingthe least squares method to estimate the parameters, so we can get the residual expression.Based on the different sample to estimate the parameter, we define the general residuals byusing the before m data which is non-polluting, at the same time we can define the recursiveresiduals by using the before i1data which have been detected. Second we can according tothe expression of the general residuals build the online monitoring statistics of the mean andvariance which based on the general residuals; at the same time we can accord to theexpression of the recursive residuals build the online monitoring statistics of the mean andvariance which based on the recursive residuals. From the theorem1to10, we can obtainedthese four statistics exist a different limit under the null hypothesis and the limit tends toinfinity under the alternative hypothesis. So we can prove that these four statistics areeffective in theory. For further illustrate the effectiveness of these statics, we can use theMonte Carlo method to simulate the experiments, so we can obtained some critical values,level of experience, potential and the average run length under the alternative hypothesis ofthese four statistics. Through the analysis of simulation results we can obtained the followingconclusions: the potential of the test affected by the location of the point, the window widthparameter h, gama and the type of the change point. The result of the variance onlinemonitoring statistics based on the recursive residual is not very obvious, but the other threestatistics are very sensitive; In order to get the higher potential and smaller average run lengthwe should use the mean online statistics based on the recursive residual which the windowwidth parameter is h0.2to test the mean change point; In order to test the variance changepoint we can use the variance online statistics based on the general residuals,if the location of the change point is close to the start point we should let the gama0.25, h0.2,if thelocation of the change point take away from the start time point we can let thegama0, h0.5,the reason why we do this is that we want to get better test result.