Estimating monotonic change in the rate and dependence parameters of INAR(1) process (Case study: IP counts data)

ABSTRACT

In this article, we consider a first-order integer-valued autoregressive (INAR(1)) model. Then, we propose change point estimators for the rate and dependence parameters in INAR(1) model using maximum likelihood estimation method when the type of change belongs to a family of monotonic changes. To monitor the process, a combined EWMA and c control chart is considered. The results show that the proposed change point estimators provide efficient estimates of the change time. At the end, to illustrate the application of the proposed estimators, a real case related to IP counts data is investigated.

KEYWORDS:

• c-EWMA control chart
• IP counts data
• Monotonic change
• pooled-adjacent-violator (PAV) algorithm
• rate and dependence parameters

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62M10
• Secondary 62F10

Acknowledgment

The authors are thankful to anonymous reviewers for valuable comments which led to significant improvement in this article.