A Beta-Gamma autoregressive process of the second-order (BGAR(2))

In this paper we present a stationary Beta-Gamma autoregressive process of the second-order which represents the generalization of the Beta-Gamma autoregressive process of the first-order [Lewis, McKenzie, Hugus, 1989. Comm. Statist. Stochastic Models 5, 1-30]. The defined process has Gamma(k,β) marginally distributions. The properties of the process are discussed. The conditional least-squares estimation and the method of moments are used. Asymptotic distributions of the estimates are given and the asymptotic confidence regions are obtained. Some numerical results of the estimations are given.