Abstract

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.

摘要

在当今的统计文献中，人们对非高斯时间序列，尤其是由非负整数（计数）组成的序列越来越感兴趣。Count 系列自然会出现在农业、经济、流行病学、金融、地质、气象和体育等领域。与自回归移动平均值是主要建模工具的平稳高斯系列不同，没有哪一类模型在计数领域占主导地位。因此，文献在某种程度上是临时演变的，开发了不同的模型类来处理特定情况。本文试图总结计数时间序列建模的当前状态。本文首先回顾了具有指定边际分布的模型，包括一些最近的发展。接下来是对状态空间方法的讨论。然后研究方法的多元扩展，并考虑贝叶斯方法来解决问题。目的是让研究人员和从业人员了解现代文献中出现的各种类型的计数时间序列模型。虽然没有详细讨论估计问题，但参考了该文献。