Statistical Modeling of Integer-valued Time Series: An Introduction

Modeling and predicting the temporal dependence and evolution of low integer-valued time series have attracted a lot of attention over the last years. This is partially due to the increasing availability of relevant high-quality data sets in various fields of applications ranging from finance and economy to medicine and ecology. It is important to stress, however, that there is no a unifying approach applicable to modeling all integer-valued time series and, consequently, the analysis of such time series has to be restricted to special classes of integer-valued models. A useful division of these models can be made as being either observation-driven or parameter-driven models.  A suitable class of observation-driven models is the one including models based on thinning operators. Models belonging to this class are obtained by replacing the multiplication in the conventional time series models by an appropriate thinning operator, along with considering a discrete distribution for the sequence of innovations in order to preserve the discreteness of the counts.

This talk aims at providing an overview of recent developments in thinning-based time series models paying particular attention to models obtained as discrete counterparts of conventional univariate and multivariate autoregressive moving average models, with either finite or infinite support. Finally, we also outline and discuss likely directions of future research.