Review of Copula for Bivariate Distributions of Zero-Inflated Count Time Series Data

Abstract

The class of bivariate integer-valued time series models, described via copula theory, is gaining popularity in the literature because of applications in health sciences, engineering, financial management and more. Each time series follows a Markov chain with the serial dependence captured using copula-based distribution functions from the Poisson and the zero-inflated Poisson margins. The copula theory is again used to capture the dependence between the two series. However, the efficiency and adaptability of the copula are being challenged because of the discrete nature of data and also in the case of zero-inflation of count time series. Likelihood-based inference is used to estimate the model parameters for simulated and real data with the bivariate integral of copula functions. While such copula functions offer great flexibility in capturing dependence, there remain challenges related to identifying the best copula type for a given application.  This paper presents a survey of the literature on bivariate copula for discrete data with an emphasis on the zero-inflated nature of the modelling. We demonstrate additional experiments on to confirm that the copula has potential as greater research area.