On first-order integer-valued autoregressive process with Katz family innovations

ABSTRACT

This paper considers the first-order integer-valued autoregressive (INAR) process with Katz family innovations. This family of INAR processes includes a broad class of INAR(1) processes with Poisson, negative binomial, and binomial innovations, respectively, featuring equi-, over-, and under-dispersion. Its probabilistic properties such as ergodicity and stationarity are investigated and the formula of the marginal mean and variance is provided. Further, a statistical process control procedure based on the cumulative sum control chart is considered to monitor autocorrelated count processes. A simulation and real data analysis are conducted for illustration.

KEYWORDS:

• INAR(1) process
• Katz family of distributions
• statistical process control
• CUSUM control chart
• average run length

Acknowledgments

We thank the referee for his/her careful reading and valuable comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) [No. 2015R1A2A2A01003894].