The bivariate integer-valued GARCH model: a Bayesian estimation framework - Verges, Yuri (2019)
An extensive literature has been developed on counting data in recent years, and the contribution that seeks the multivariate approach to this problem is still small. This paper aims to analyze in greater depth and perform the Bayesian estimation of the bivariate INGARCH model proposed in Cui and Zhu [2017], where the autoregression studied in Liu [2012] is extended to treat negatively correlated events. Since the probability function proposed in Lakshminarayana et al. [1999] demands some attention to the non-infringement of the probability axioms, a thorough analysis of this new distribution has been performed. For the Bayesian estimation procedure, the Random Walk Metropolis-Hastings algorithm was applied, and tunning was chosen as in one of Bennett et al. [1996] approaches. An exhaustive analysis on simulated data was performed for the real understanding of how the proposed model behaves, and, aiming at the application in real data, a study on the Pittsburgh crime data and another on the number of trades for the futures contracts of Euro and British Pound at traded CME (Chigado Mechandile Exchange) were implemented.