Drift Change Point Estimation in Autocorrelated Poisson Count Processes Using MLE Approach

Change point estimation in the area of statistical process control has received considerable attentions. The assumption of uncorrelated observations is unrealistic in many cases. However, less attention has been given to change point estimation in autocorrelated processes. Among the autocorrelated processes, count data are most widely used in real-world. Different applications of count data are discussed by many researchers such as syndromic surveillance data in healthcare, accident monitoring systems and multi-item pricing models in management science. Poisson distribution for count processes and the first-order integer-valued autoregressive (INAR (1)) model are considered in this paper. We use a combined EWMA and C control chart to monitor the process. We propose change point estimators for the rate and dependence parameters with linear trend under different magnitudes of shifts. For this purpose, Newton's method is used to estimate the paramaters of the process after the change. Then, we develop the maximum likelihood estimators to estimate the real time of change in the parameters. The accuracy and prescision of the proposed MLE estimators are evaluated through simulation studies. In addition, the performance of the proposed estimators is compared with the ones proposed for step change under linear drift. The simulation results confirm that the change point estimators are effective in identifying linear trend in the process parameters. Finally, application of the proposed change point estimators is illustrated through an IP counts data real case.