A class of bivariate integer-valued time series models was constructed via copula theory. Each series follows a Markov chain with the serial dependence captured using copula-based transition probabilities from the Poisson and the zero-inflated Poisson (ZIP) margins. The copula theory was also used again to capture the dependence between the two series using either the bivariate Gaussian or “t-copula” functions. Such a method provides a flexible dependence structure that allows for positive and negative correlation, as well. In addition, the use of a copula permits applying different margins with a complicated structure such as the ZIP distribution. Likelihood-based inference was used to estimate the models’ parameters with the bivariate integrals of the Gaussian or t-copula functions being evaluated using standard randomized Monte Carlo methods. To evaluate the proposed class of models, a comprehensive simulated study was conducted. Then, two sets of real-life examples were analyzed assuming the Poisson and the ZIP marginals, respectively. The results showed the superiority of the proposed class of models.
Original Publication Citation
Alqawba, M., Fernando, D., & Diawara, N. (2021). A class of copula-based bivariate poisson time series models with applications. Computation, 9(10), 1-12, Article 108. https://doi.org/10.3390/computation9100108
Alqawba, Mohammed; Fernando, Dimuthu; and Diawara, Norou, "A Class of Copula-Based Bivariate Poisson Time Series Models with Applications" (2021). Mathematics & Statistics Faculty Publications. 195.