Poisson limit of an inhomogeneous nearly critical INAR(1) model

This paper considers non-negative integer-valued autoregressive processes where the autoregression parameter is close to unity. We consider the asymptotics of this `near unit root' situation. The local asymptotic structure of the likelihood ratios of the model is obtained, showing that the limit experiment is Poissonian. To illustrate the statistical consequences we discuss efficient estimation of the autoregression parameter and efficient testing for a unit root.

We investigate joint temporal and contemporaneous aggregation of N independent copies of strictly stationary INteger-valued AutoRegressive processes of order 1 (INAR(1)) with random coefficient $\alpha\in(0,1)$ and with idiosyncratic Poisson innovations. Assuming that $\alpha$ has a density function of the form $\psi(x) (1 - x)^\beta$, $x \in (0,1)$, with $\beta\in(-1,\infty)$ and $\lim_{x\uparrow 1} \psi(x) = \psi_1 \in (0,\infty)$, different limits of appropriately centered...

We suggest an INARMA(1, 1) model with Poisson marginals which extends the INAR(1) in a similar way as the INGARCH(1, 1) does for the INARCH(1) model. The new model is equivalent to a binomially thinned INAR(1) process. This allows us to obtain some of its stochastic properties and use inference methods for hidden Markov models. The model is compared to various other models in two case studies.

We discuss joint temporal and contemporaneous aggregation of $N$ independent copies of strictly stationary INteger-valued AutoRegressive processes of order 1 (INAR(1)) with random coefficient $\alpha\in(0,1)$ and with idiosyncratic Poisson innovations. Assuming that $\alpha$ has a density function of the form $\psi(x)(1 - x)^\beta$, $x\in(0,1)$, with $\lim_{x\uparrow 1}\psi(x) = \psi_1 \in(0,\infty)$, different limits of appropriately centered and scaled aggregated partial su...

In this paper, we introduce the first-order integer-valued autoregressive (INAR(1)) model, with Poisson-Lindley innovations based on power series thinning operator. Some mathematical features of this process are given and estimating the parameters is discussed by three methods; conditional least squares, Yule-Walker equations and conditional maximum likelihood.Then the results are studied for three special cases of power series operators. Finally, some numerical results are p...

The random coefficient integer-valued autoregressive process was introduced by Zheng, Basawa, and Datta. 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.

Strictly stationary INAR(1) ("integer-valued autoregressive processes of order 1") with Poisson innovations are "interlaced rho-mixing".

An extension of the RINAR(1) process for modelling discrete-time dependent counting processes is considered. The model RINAR(p) investigated here is a direct and natural extension of the real AR(p) model. Compared to classical INAR(p) models based on the thinning operator, the new models have several advantages: simple innovation structure ; autoregressive coefficients with arbitrary signs ; possible negative values for time series ; possible negative values for the autocorre...

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 unstable autoregressive processes of order p. An application for Boston armed robberies...

We discuss joint temporal and contemporaneous aggregation of $N$ independent copies of strictly stationary AR(1) and INteger-valued AutoRegressive processes of order 1 (INAR(1)) with random coefficient $\alpha \in (0, 1)$ and idiosyncratic innovations. Assuming that $\alpha$ has a density function of the form $\psi(x) (1 - x)^\beta$, $x \in (0, 1)$, with $\lim_{x\uparrow 1} \psi(x) = \psi_1 \in (0, \infty)$, different Brownian limit processes of appropriately centered and sca...