Binomial thinning models for integer time series

Abstract

This article considers some simple observation-driven time series models for counts. We provide a brief description of the class of integer-valued autoregressive (INAR) and integer-valued moving average (INMA) processes. These classes of models may be attractive when the data exhibit a significant serial dependence structure. We, therefore, briefly review various testing procedures useful for assessing the serial correlation in the data. Once it is established that the data are not serially independent, suitable INAR or INMA processes may be employed to model the data. In the important first order INAR model, we discuss various methods of estimating the structural parameters of the process. We also give a short account of the extension of some of these estimation procedures to second order INAR models. Moving average counterparts of both models are also entertained. Throughout, the models and methods are illustrated in the context of a famous data set from the branching process literature that turns out to be surprisingly difficult to model satisfactorily.

Thinning operations for modeling time series of counts—a survey

“…Finally, it should be mentioned that higher order members of the INARMA family have also been discussed in the literature; for a recent review, see Jung and Tremayne (2006a). But while the INAR(1) recursion involves one thinning operation only, the higher order models need more than one thinning operation at once.…”

Useful models for time series of counts or simply wrong ones?

“…innovation process independent of R t (·). This class of models has received wide attention in recent years, see inter alia Brännäs (1994), Jung and Tremayne (2006a), and Weiß (2008) and the references therein. McKenzie (2003) provides a fairly comprehensive survey at that time.…”

Effects of Overdispersion on Testing for Serial Dependence in the Time Series of Counts Data

“…(iii) As mentioned, the limiting distribution of Q ac f (k) and Q pac f (k) are the χ 2 distribution with the degree of freedom k under the null of i.i.d.variables (Mills and Seneta, 1989;Jung and Tremayne, 2006). …”