On random coefficient INAR(1) processes

Abstract

The random coefficient integer-valued autoregressive process was introduced by Zheng, Basawa, and Datta in [54]. 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.

Thinning-based models in the analysis of integer-valued time series: a review

“…r.v's each one taking values in the interval [0; 1), and (Z t ) is a sequence of i.i.d. integer-valued non-negative r.v's, independent of (ϕ t ), were considered by Zhang and Wang (2015), Roitershtein and Zhong (2013), Bakouch and Ristić (2010), Gomes andCanto e Castro (2009) andZheng et al (2007). Gomes andCanto e Castro (2009) andZheng et al (2007) proved that if E(Z t ) and V(Z t ) are finite, then the condition E(ϕ 2 t ) < 1, ∀t ∈ Z Z, ensures that there exists a unique nonnegative integer-valued weakly stationary process satisfying (3.2).…”

Quasistochastic matrices and Markov renewal theory

“…The case when (A n ) n∈Z forms an irreducible stationary Markov chain taking values in a finite subset S of R and the B n are i.i.d. and independent of the A n was treated by de Saporta [17], see also [25,26] for the more general case of continuous state space S . Let us take a closer look at the situation treated in [17], for simplicity confining ourselves to the case when S ⊂ (0, ∞), but allowing that S is an infinite countable set.…”

“…The case where {A n } n∈Z forms an irreducible stationary Markov chain taking values in a finite subset S of R, and the B n are i.i.d. and independent of the A n was treated by de Saporta [13]; see also [22,23] for the more general case of continuous state space S.…”

Interval Estimation of Random Coefficient Integer-Valued Autoregressive Model Based on Mean Empirical Likelihood Method

“…In recent years, RCINAR(1) models have been discussed in many studies. Roitershtein and Zhong [12] studied the asymptotic behaviour of the RCINAR(1) model in the case where the additive term in the underlying random linear recursion belongs to the domain of attraction of a stable law. Zhang and Wang [13] presented the explicit expressions for the higher-order moments and cumulants of the RCINAR(1) process.…”