随机系数自回归模型变均值点在线监测与应用

对随机系数自回归模型的变均值点进行在线监测时, 如果变均值点的位置远离开始监测点, 则平均地说, 需要较长的运行时间方能检测到该变均值点. 为此, 笔者引进一个窗宽参数, 提出了一种改进的在线监测方法. 给出了监测统计量在原假设下的极限分布, 并证明了此方法的一致性. 模拟结果显示新方法明显优于已有的方法. 最后将该方法应用于两组股票价格均值点的监测问题中, 说明了方法的有效性.

Online monitoring of mean change point in a random coefficient autoregressive model

In online monitoring the varying mean point of a random coefficient autoregressive model, if the varied mean point is far in position from the starting point of monitoring, it will take longer operation time in average to detect that varied mean point. To deal with this problem, we propose an improved procedure by introducing a window-width parameter. The asymptotic distribution of the monitoring statistic under null hypothesis is derived and its consistency is proved. Simulations show that our method is more powerful than the existing ones. This method has been applied to two groups of stock data for monitoring the variations of the mean points; results validate the effectiveness of the proposed procedure.