A change point estimator in monitoring the parameters of a multivariate IMA(1, 1) model

Modern production process is a very complex structure combined observations which are correlated with several factors. When the error signal occurs in the process, it is very difficult to know the root causes of an out-of-control signal because of insufficient information. However, if we know the time of the change, the system can be controlled more easily. To know it, we derive a maximum likelihood estimator (MLE) of the change point in a process when observations are from a multivariate IMA(1,1) process by monitoring residual vectors of the model. In this paper, numerical results show that the MLE of change point is effective in detecting changes in a process.