A Binomial Integer-Valued ARCH Model

IF 1.2 4区数学 International Journal of Biostatistics Pub Date : 2016-11-01 DOI:10.1515/ijb-2015-0051

M. Ristić, C. Weiß, Ana D Janjić

引用次数: 24

Abstract

Abstract We present an integer-valued ARCH model which can be used for modeling time series of counts with under-, equi-, or overdispersion. The introduced model has a conditional binomial distribution, and it is shown to be strictly stationary and ergodic. The unknown parameters are estimated by three methods: conditional maximum likelihood, conditional least squares and maximum likelihood type penalty function estimation. The asymptotic distributions of the estimators are derived. A real application of the novel model to epidemic surveillance is briefly discussed. Finally, a generalization of the introduced model is considered by introducing an integer-valued GARCH model.

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二项整数值ARCH模型

摘要提出了一种整数值ARCH模型，该模型可用于对欠分散、等分散或过分散的计数时间序列进行建模。所引入的模型具有条件二项分布，并被证明是严格平稳和遍历的。通过条件极大似然、条件最小二乘和极大似然罚函数估计三种方法对未知参数进行估计。导出了估计量的渐近分布。最后简要讨论了该模型在流行病监测中的实际应用。最后，通过引入整数值GARCH模型，对所引入的模型进行了推广。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal of Biostatistics Mathematics-Statistics and Probability

CiteScore

2.30

自引率

8.30%

发文量

期刊介绍： The International Journal of Biostatistics (IJB) seeks to publish new biostatistical models and methods, new statistical theory, as well as original applications of statistical methods, for important practical problems arising from the biological, medical, public health, and agricultural sciences with an emphasis on semiparametric methods. Given many alternatives to publish exist within biostatistics, IJB offers a place to publish for research in biostatistics focusing on modern methods, often based on machine-learning and other data-adaptive methodologies, as well as providing a unique reading experience that compels the author to be explicit about the statistical inference problem addressed by the paper. IJB is intended that the journal cover the entire range of biostatistics, from theoretical advances to relevant and sensible translations of a practical problem into a statistical framework. Electronic publication also allows for data and software code to be appended, and opens the door for reproducible research allowing readers to easily replicate analyses described in a paper. Both original research and review articles will be warmly received, as will articles applying sound statistical methods to practical problems.