Recent advancements in integer-valued autoregressive models for count data time series: A comprehensive review

Count data time series, characterized by non-negative integer values, frequently arise across diverse domains, including finance, public health, economics, epidemiology, and environmental sciences. Such series often exhibit characteristics such as equidispersion, overdispersion, underdispersion, and zero-inflation/deflation. Failure to appropriately account for these features can result in biased parameter estimates and misleading statistical inference. This review presents a comprehensive overview of recent methodological developments in integer-valued autoregressive (INAR) models, with particular emphasis on thinning operators, estimation methods, and model extensions. A systematic literature search was conducted using electronic databases, including Scopus and Google Scholar, to identify relevant studies published between 2010 and 2024. Recent research has primarily focused on the development of novel thinning operators and flexible innovation distributions aimed at constructing unified modeling frameworks capable of accommodating multiple characteristics of count data simultaneously. This review highlights prevailing research trends, identifies existing methodological gaps, and outlines promising directions for future research in count data time series modeling.