Count Time Series: A Methodological Review

• 成果类型: Review
• 署名作者: Davis, Richard A.; Fokianos, Konstantinos; Holan, Scott H.; Joe, Harry; Livsey, James; Lund, Robert; Pipiras, Vladas; Ravishanker, Nalini
• 署名单位: Columbia University; University of Cyprus; University of Missouri System; University of Missouri Columbia; University of British Columbia; University of California System; University of California Santa Cruz; University of North Carolina; University of North Carolina Chapel Hill; University of Connecticut
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2021.1904957
• 发表日期: 2021
• 页码: 1533-1547
• 关键词: maximum-likelihood-estimation; moving-average processes; specified marginals; Poisson regression; copula models; distributions; ergodicity; dependence; inference; mixtures

摘要

A growing interest in non-Gaussian time series, particularly in series comprised of nonnegative integers (counts), is taking place in today's statistics literature. Count series naturally arise in fields, such as agriculture, economics, epidemiology, finance, geology, meteorology, and sports. Unlike stationary Gaussian series where autoregressive moving-averages are the primary modeling vehicle, no single class of models dominates the count landscape. As such, the literature has evolved somewhat ad-hocly, with different model classes being developed to tackle specific situations. This article is an attempt to summarize the current state of count time series modeling. The article first reviews models having prescribed marginal distributions, including some recent developments. This is followed by a discussion of state-space approaches. Multivariate extensions of the methods are then studied and Bayesian approaches to the problem are considered. The intent is to inform researchers and practitioners about the various types of count time series models arising in the modern literature. While estimation issues are not pursued in detail, reference to this literature is made.