Over the past few years, interest has increased in models defined on positive and negative integers. Several application areas lead to data that are differences between positive integers. Some important examples are price changes measured discretely in financial applications, pre- and posttreatment measurements of discrete outcomes in clinical trials, the difference in the number of goals in sports events, and differencing of count-valued time series. This review aims at bringing together a wide range of models that have appeared in the literature in recent decades. We provide an extensive review on discrete distributions defined for integer data and then consider univariate and multivariate time-series models, including the class of autoregressive models, stochastic processes, and ARCH-GARCH– (autoregressive conditionally heteroskedastic–generalized autoregressive conditionally heteroskedastic–) type models.

中文翻译：

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 整数数据的模型


在过去的几年里，人们对在正整数和负整数上定义的模型的兴趣有所增加。几个应用领域会导致数据是正整数之间的差异。一些重要的例子是在金融应用中离散测量的价格变化、临床试验中离散结果的治疗前和治疗后测量、体育赛事中进球数的差异以及计数值时间序列的差异。本综述旨在汇集近几十年来文献中出现的各种模型。我们对为整数数据定义的离散分布进行了广泛的回顾，然后考虑了单变量和多变量时间序列模型，包括自回归模型、随机过程和 ARCH-GARCH– （自回归条件异方差-广义自回归条件异方差–） 类型模型。