Asymptotic inference for nearly unstable INAR(1) models

The rst{order integer{valued autoregressive (INAR(1)) process is investigated, where the autoregressive coecient is close to one. It is shown that the limiting distri-bution of the conditional least{squares estimator for this coecient is normal and, in contrast to the familiar AR(1) process, the rate of convergence is n3=2. Finally, the nearly critical Galton{Watson process with unobservable immigration is discussed. Keywords. Discrete time series, INAR(1) model, stable and nearly unstable mod-els, conditional least squares estimator, asymptotic distribution, Galton{Watson pro-cess.