Estimating the Change Point of Correlated Poisson Count Processes

ABSTRACT

Knowing the time of change would narrow the search to find and identify the variables disturbing a process. The knowledge of the change point can greatly aid practitioners in detecting and removing the special cause(s). Count processes with an autocorrelation structure are commonly observed in real-world applications and can often be modeled by the first-order integer-valued autoregressive (INAR) model. The most widely used marginal distribution for count processes is Poisson. In this study, change-point estimators are proposed for the parameters of correlated Poisson count processes. To do this, Newton's method is first used to approximate the parameters of the process. Then, maximum likelihood estimators of the process change point are developed. The performances of these estimators are next evaluated when they are employed in a combined exponentially weighted moving average (EWMA) and c scheme. Finally, for the rate parameter, the proposed estimator is compared with the estimator developed for independent observations.

KEYWORDS:

• change-point estimation
• maximum likelihood
• poisson counts
• autocorrelation
• INAR(1)

ACKNOWLEDGMENT

The authors are thankful for constructive comments from the anonymous reviewers, which certainly improved the presentation of the article.

Notes

lc: lower control limit of the c chart.

uc: upper control limit of the c chart.

le: lower control limit of the EWMA chart.

ue: upper control limit of the EWMA chart.

The bold values show the estimated time of the change.

The bold values show the estimated time of the change.