Asymptotic behavior of unstable INAR(p) processes

Asymptotic Behaviour of Estimators of the Parameters of Nearly Unstable INAR(1) Models

A sequence of first–order integer–valued autoregressive type (INAR(1)) processes is investigated, where the autoregressive type coefficients converge to 1. It is shown that the limiting distribution of the joint conditional least squares estimators for this coefficient and for the mean of the innovation is normal. Consequences for sequences of Galton–Watson branching processes with unobservable...

Asymptotic distribution of the Yule-Walker estimator for INAR(p) processes

The INteger-valued AutoRegressive (INAR) processes were introduced in the literature by Al-Osh and Alzaid (1987) and McKenzie (1988) for modelling correlated series of counts. These processes have been considered as the discrete counter part of AR processes, but their highly nonlinear characteristics lead to some statistically challenging problems, namely in parameter estimation. Several estima...

Asymptotic Behavior of Multivariate Reward Processes with Nonlinear Reward Functions

Asymptotic Inference for Nearly Unstable Inar(1) Models

The first–order integer–valued autoregressive (INAR(1)) process is investigated, where the autoregressive coefficient is close to one. It is shown that the limiting distribution of the conditional least–squares estimator for this coefficient is normal and, in contrast to the familiar AR(1) process, the rate of convergence is n. Finally, the nearly critical Galton–Watson process with unobservabl...

On random coefficient INAR(1) processes

The random coefficient integer-valued autoregressive process was introduced by Zheng, Basawa, and Datta in [55]. In this paper we study the asymptotic behavior of this model (in particular, weak limits of extreme values and the growth rate of partial sums) in the case where the additive term in the underlying random linear recursion belongs to the domain of attraction of a stable law. MSC2000: ...