Resumen de Analysis of zero-and-one inflated bounded count time series with applications to climate and crime data
Yao Kang, Shuhui Wang, Dahui Wang, Fukang Zhu
This article introduces a new version of first-order binomial autoregressive (BAR(1)) process with zero-and-one inflated binomial marginals using the idea of hidden Markov models, which contains the BAR(1) and other existing processes as special cases. Stochastic properties of the new model are investigated and model parameters are estimated by the probability-based, quasi-maximum likelihood, maximum likelihood and Bayesian methods. A binomial one-inflation index is constructed and further utilized to develop a method to test whether zero and/or one inflation with respect to a BAR(1) model. We also give the asymptotic distribution of the corresponding test statistics under the null hypothesis. Applications to rainy-days and assaults-on-officers counts are conducted, which shows that the proposed model can accurately capture zero-inflation, one-inflation and overdispersion characteristics of the data. The predictive distributions are employed to identify the occurrence of anomalies and then establish early warning system of risk.
