Computational methods for a copula-based Markov chain model with a binomial time series

A copula-based Markov chain model can flexibly capture serial dependence in a time series. However, the computational developments for copula-based Markov models remain insufficient for discrete marginal models compared with continuous ones. In this article, we develop computational methods for a binomial time series under the Clayton and Joe copulas. The methods include the data-generation, parameter estimation, model selection, and goodness-of-fit tests. We implement the methods in our R package Copula.Markov (https://CRAN.R-project.org/package=Copula.Markov). We conduct simulations to see the performance of the developed methods. Finally, the proposed method is illustrated by a real dataset.