Thinning Based Models: A Comprehensive Literature Review

Abstract

Count time series are non-negative values that are collected in chronological order over time. This type of series posses characteristics such as under-dispersion, equi-dispersion, over-dispersion, and zero-inflation (deflation) and arise naturally from several areas of human endeavour. The quest for proper modelling of such series, so as to avoid biased estimation and misleading predictions, gave rise to thinning base models. In this paper, a comprehensive literature review on thinning based models is made. Different thinning based models such as integer-valued autoregressive models - with details on integer-valued autoregressive model of first order, its extensions-, integer-valued moving average and some other models that are related to these models were reviewed. The review, in addition to containing robust information on the thinning operators employ when constructing thinning based models, paid particular attention to integer-valued autoregressive models for the various dispersion structure (under-dispersion, equi-dispersion and over-dispersion) that may be present in a given count time series and for zero-inflated (deflated) count time series. Test of hypothesis required for the application of integer-valued autoregressive models, methods of estimation use and forecast functions for the models were discussed. From the review some possible areas for future research on thinning based models were suggested.