Drift Change Point Estimation in the rate and dependence Parameters of Autocorrelated Poisson Count Processes Using MLE Approach: An Application to IP Counts Data

Abstract

Change point estimation in the area of statistical process control has received considerable attentions in the recent decades because it helps process engineer to identify and remove assignable causes as quickly as possible. On the other hand, improving in measurement systems and data storage, lead to taking observations very close to each other in time and as a result increasing autocorrelation between observations. 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, and IP counts data. In this paper, we consider Poisson distribution for count processes and the first-order integer-valued autoregressive (INAR (1)) model. Then, we propose change point estimators for the parameters under linear trend, when observation arises from an autocorrelated Poisson count process using maximum likelihood estimators. We use a combined EWMA and c control chart to monitor the process. 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.