Maximum likelihood estimation of the change point in stationary state of auto regressive moving average (ARMA) models, using SVD-based smoothing

Abstract

The change point estimation concept is usually useful in time series models. This concept helps to decrease the decision making or production costs by monitoring the stock market and production lines. It is also applied in several fields such as Financing and Quality Control. In this paper, it is assumed that the ARMA (1) model exists between the sample statistics of $\overline{x}$ control chart. A maximum likelihood technique is developed to estimate the change point at which the stationary ARMA (1) model changes into a non-stationary process. For the estimation of unknown parameters after the change point, the Smoothing of Dynamic Linear Model has been used based on singular value decomposition. It is assumed that there exists a correlation between sample statistics. Simulation results show the effectiveness of the estimators proposed in this paper to estimate the change point of the stationary state in ARMA (1) model. An example is provided to illustrate the application.

Keywords:

• Change point estimation
• ARMA
• (1) model
• dynamic linear model (DLM)
• maximum likelihood estimation
• singular value decomposition (SVD)
• smoothing