Article2016

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

34 citations0/0 files storedJournal of Statistical Computation and Simulation

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Advanced Statistical Process Monitoring Probability and Statistical Research Statistical Distribution Estimation and Applications

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.

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References

1954CONTINUOUS INSPECTION SCHEMES 1972An Approach to the Probability Distribution of Cusum Run Length 2001Cusum Charts for Monitoring an Autocorrelated Process 2007SPC Procedures for Monitoring Autocorrelated Processes 2009CUSUM Monitoring of First-Order Integer-Valued Autoregressive Processes of Poisson Counts 2007Controlling correlated processes of Poisson counts 2009Parameter change test for random coefficient integer‐valued autoregressive processes with application to polio data analysis

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2018CUSUM test for general nonlinear integer-valued GARCH models: comparison study 2019Improved CUSUM monitoring of Markov counting process with frequent zeros 2017Monitoring parameter shift with Poisson integer-valued GARCH models 2021Recent progress in parameter change test for integer-valued time series models 2021Exact Run Length Evaluation on a Two-Sided Modified Exponentially Weighted Moving Average Chart for Monitoring Process Mean

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