In this paper, we consider the structural change in a class of discrete valued time series, where true conditional distribution observations is assumed to be unknown. The mean process depends on parameter θ∗ which may over time. We provide sufficient conditions for consistency and asymptotic normality Poisson quasi-maximum likelihood estimator (QMLE) model. an epidemic change-point detection pr...

This paper deals with model selection for a general class of integer-valued time series. We propose penalized criterion based on the Poisson quasi-likelihood model. Under certain regularity conditions, consistency procedure as well and asymptotic normality estimator selected are established. Simulation experiments conducted some classical models such negative binomial linear nonlinear dynamics....

This paper develops likelihood-based methods for estimation, inference, model selection, and forecasting of continuous-time integer-valued trawl processes. The full likelihood processes is, in general, highly intractable, motivating the use composite methods, where we consider pairwise lieu likelihood. Maximizing data yields an estimator parameter vector model, prove consistency and, short memo...

Abstract When dealing with time series outlying and atypical data, a commonly used approach is to develop models based on heavy-tailed distributions. The literature coping continuous-valued extreme observations well explored. However, current modelling integer-valued data heavy-tailedness less considered. state of the art research this topic presented by Gorgi (J R Stat Soc Ser B (Stat Methodol...

‎Recently a first-order Spatial Integer-valued Autoregressive‎ ‎SINAR(1,1) model was introduced to model spatial data that comes‎ ‎in counts citep{ghodsi2012}‎. ‎Some properties of this model‎ ‎have been established and the Yule-Walker estimator has been‎ ‎proposed for this model‎. ‎In this paper‎, ‎we introduce the...

Fermat’s Little Theorem states that xp z(modp) for z E N and prime p, and so identifies an integer-valued polynomial (IVP) g,(z) (zr x)/p. Presented here are IVP’s gn for non-prime n that complete the sequence {gn n E N} in a natural way. Also presented are characterizations of the gn’S and an indication of the ideas from topological dynamics and algebra that brought these matters to our attent...