Comments on: Some recent theory for autoregressive count time series

Abstract

The paper of Pr. Dag Tjostheim is a great and comprehensive study addressing mainly the asymptotic properties of a class of GLMs with integer values: Xt = Pt (λt ), where Pt (·) is a Poisson process with rate one, and λt is a deterministic function of the past of the bivariate process Yt = (Xt , λt ). This is an alternative to GARCH type models for count data where Xt |Ft−1 ∼P(λt ), with P(·) the Poisson distribution. In fact this model, considered in Doukhan et al. (2012b), implies that for some deterministic function f : (N×R+)∞ →R+, the rate λt satisfies λt = f (Xt−1, λt−1,Xt−2, λt−2, . . .).