Change point estimation is a useful concept in time series models that could be applied in several fields such as financing, quality control. It helps to decrease costs of decision making and production by monitoring stock market and production lines, respectively. In this paper, the maximum likelihood technique is developed to estimate change point at which the stationary AR(1) model changes to a nonstationary process. Filtering and smoothing of dynamic linear model are used to estimate unknown parameters after change point. We also assume that correlation exists between samples' statistics. Simulation results show the effectiveness of the proposed estimators to estimate the change point of stationary. In addition based on Shewhart control chart, filtering has a better accuracy in comparison to smoothing. A real example is provided to illustrate the application.

In this paper, for the first time, the subject of change point estimation has been utilized in the stationary state of auto regressive moving average (ARMA) (1, 1). In the monitoring phase, in case the features of the question pursue a time series, i.e., ARMA(1,1), on the basis of the maximum likelihood technique, an approach will be developed for the estimation of the stationary state's change point. To estimate unidentified parameters following the change point, the dynamic linear model's filtering was utilized on the basis of the singular decomposition of values. The proposed model has wide applications in several fields such as finance, stock exchange marks and rapid production. The results of simulation showed the suggested estimator's effectiveness. In addition, a real example on stock exchange market is offered to delineate the application.