EM estimation for bivariate mixed poisson INAR(1) claim count regression models with correlated random effects

Abstract This article considers bivariate mixed Poisson INAR(1) regression models with correlated random effects for modelling correlations of different signs and magnitude among time series types claim counts. is the first that proposed family used in a statistical or actuarial context. For expository purposes, count Lognormal Gamma paired via Gaussian copula are presented as competitive alternatives to classical Negative Binomial model which only allows positive dependence between responses. Our main achievement we develop novel alternative Expectation-Maximization type algorithms maximum likelihood estimation parameters demonstrated perform satisfactory when fitted Local Government Property Insurance Fund data from state Wisconsin.