AR(p)模型参数变点的残差CUSUM在线监测

Monitoring Parameter Change in AR(p) Time Series Model Based on CUSUM of Residuals

针对AR(p)模型参数变点的在线监测问题,首先给出参数的最小二乘估计;其次构造参数变点的残差CUSUM监测统计量,并得到原假设和备择假设下监测统计量的极限性质;最后通过Monte Carlo方法给出监测统计量的经验水平和经验势,说明了该方法的有效性.

To study the on-line monitoring problem of parameter change point in AR(p) model,firstly,the leastsquares estimation of the parameters is given. Secondly,CUSUM of residuals monitoring statistic of the parameterchange points is constructed,and the limit properties of the monitoring statistic are obtained under the null hypothesisand the alternative hypothesis. Finally,the Monte Carlo method is used to give the empirical level and empiricalpower of the monitoring statistic,and the effectiveness of the method is explained.