Bayesian analysis of the p-order integer-valued AR process with zero-inflated Poisson innovations

Abstract

In recent years, there has been a considerable interest to study count time series with a dependence structure and appearance of excess of zeros values. Such series are commonly encountered in diverse disciplines, such as economics, financial research, environmental science, public health, among others. In this paper, we propose a stationary p-order integer-valued autoregressive process with zero-inflated Poisson innovations, called the ZINAR(p) times series model. We study some of its theoretical properties and develop a Markov chain Monte Carlo (MCMC) algorithm for inferring parameters from Bayesian perspectives. Finally, we demonstrate the utility of proposed ZINAR(p) model through simulated and real data examples.

Keywords:

• Count time series
• ZINAR(p)
• Bayesian estimation
• prediction
• MCMC algorithm

2010 Mathematics Subject Classification:

• 62M10

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

We thank the SSI of the Federal University of Pernambuco (UFPE), Brazil, for providing the Assaults dataset. Aldo M. Garay would like to acknowledge the support of the National Council for Scientific and Technological Development (Conselho Nacional de Desenvolvimento Científico e Tecnológico), CNPq-Brazil [grant number 420082/2016-6]. T.I. Lin would like to acknowledge the support of the Ministry of Science and Technology of Taiwan [grant number 107-2118-M-005-002-MY2].