A Conway-Maxwell-Poisson-Binomial AR(1) Model for Bounded Time Series Data

• Published in: Entropy (Basel, Switzerland) Vol. 25; no. 1; p. 126
• Main Authors: Chen, Huaping, Zhang, Jiayue, Liu, Xiufang
• Format: Journal Article
• Language: English
• Published: Switzerland MDPI AG 07-01-2023; MDPI
• Subjects: Asymptotic properties; Autoregressive models; Autoregressive processes; Binomial distribution; bounded time series; CMPB thinning operator; CMPBAR model; equi-dispersion; Maximum likelihood estimates; Normality; over-dispersion; Probability; Random variables; Time series; under-dispersion; bounded time series; equi-dispersion; over-dispersion; CMPB thinning operator; CMPBAR model; under-dispersion
• ISSN: 1099-4300; 1099-4300
• DOI: 10.3390/e25010126

Binomial autoregressive models are frequently used for modeling bounded time series counts. However, they are not well developed for more complex bounded time series counts of the occurrence of
exchangeable and dependent units, which are becoming increasingly common in practice. To fill this gap, this paper first constructs an exchangeable Conway-Maxwell-Poisson-binomial (CMPB) thinning operator and then establishes the Conway-Maxwell-Poisson-binomial AR (CMPBAR) model. We establish its stationarity and ergodicity, discuss the conditional maximum likelihood (CML) estimate of the model's parameters, and establish the asymptotic normality of the CML estimator. In a simulation study, the boxplots illustrate that the CML estimator is consistent and the qqplots show the asymptotic normality of the CML estimator. In the real data example, our model takes a smaller AIC and BIC than its main competitors.