Asymptotic Inference for Nearly Unstable Inar(1) Models

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 behavior of unstable INAR(p) processes

In this paper the asymptotic behavior of an unstable integer-valued autoregressive model of order p (INAR(p)) is described. Under a natural assumption it is proved that the sequence of appropriately scaled random step functions formed from an unstable INAR(p) process converges weakly towards a squared Bessel process. We note that this limit behavior is quite different from that of familiar unst...

Asymptotic Inference for a Nearly Unstable Sequence of Stationary Spatial Ar Models

Title : ASYMPTOTIC INFERENCE FOR NEARLY UNSTABLE AR ( p ) PROCESSES

In this paper nearly unstable AR(p) processes (in other words, models with characteristic roots near the unit circle) are studied. Our main aim is to describe the asymptotic behaviour of the least squares estimators of the coefficients. A convergence result is presented for the general complex-valued case. The limit distribution is given by the help of some continuous time AR processes. We appl...

Modelling Time Series of Counts: an Inar Approach

Abstract. Time series of counts arise when the interest lies on the number of certain events occurring during a specified time interval. Many of these data sets are characterized by low counts, asymmetric distributions, excess zeros, over dispersion, ruling out normal approximations. Several approaches and diversified models that explicitly account for the discreteness of the data have been con...