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Integer-valued autoregressive models for counts showing underdispersion

机译：整数值自回归模型，用于显示分散不足的计数

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摘要

The Poisson distribution is a simple and popular mode! for count-data random variables, but it suffers from the equidispersion requirement, which is often not met in practice. While models for ovcrdisperscd counts have been discussed intensively in the literature, the opposite phenomenon, underdispersion, has received only little attention, especially in a time series context. We start with a detailed survey of distribution models allowing for underdispersion, discuss their properties and highlight possible disadvantages. After having identified two model families with attractive properties as well as only two model parameters, we combine these models with the INAR(1) model (integer-valued autoregressive), which is particularly well suited to obtain auotocorrelated counts with underdispersion. Properties of the resulting stationary INAR(1) models and approaches for parameter estimation are considered, as well as possible extensions to higher order autoregressions. Three real-data examples illustrate the application of the models in practice.
机译：泊松分布是一种简单而流行的模式！对于计数数据随机变量，但存在等分散性要求，在实践中通常无法满足。尽管文献中对分散分散数的模型进行了深入讨论，但相反的现象，分散不足，很少受到关注，特别是在时间序列中。我们从对分布模型的详细调查开始，以考虑分散不足，讨论它们的特性并强调可能存在的缺点。在确定了两个具有吸引人的特性的模型系列以及仅两个模型参数之后，我们将这些模型与INAR（1）模型（整数值自回归）结合起来，该模型特别适合获得色散不足的自动相关计数。考虑了所得固定INAR（1）模型的性质和用于参数估计的方法，以及对更高阶自回归的可能扩展。三个真实数据示例说明了模型在实践中的应用。

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