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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2026, Vol. 43 ›› Issue (2): 358-372.doi: 10.3969/j.issn.1005-3085.2026.02.011cstr: 32411.14.cjem.CN61-1269/O1.2026.02.011

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二项混合整数值GARCH模型

毛惠玉,  丁大力   

  1. 长春工程学院理学院，长春  130021
  • 收稿日期:2023-04-27 接受日期:2023-10-16 出版日期:2026-04-15 发布日期:2026-06-15

A Binomial Mixture Integer-valued GARCH Model

MAO Huiyu,  DING Dali   

  1. School of Science, Changchun Institute of Technology, Changchun 130021
  • Received:2023-04-27 Accepted:2023-10-16 Online:2026-04-15 Published:2026-06-15

摘要：

有限取值的整数值时间序列在实践中普遍存在，而且很多时间序列都在边际分布或者条件分布上呈现出多峰特征，但是大部分整数值模型都假设序列由单峰的新息序列驱动。混合模型在过度离散和多峰态数据上往往表现较好，针对有限取值的整数值时间序列，考虑了一类混合模型，建立了二项分布混合整数值GARCH(B-MINGARCH)模型，此模型含有一类严平稳与遍历的二项混合整数值ARCH(B-MINARCH)模型。给出了混合模型一、二阶平稳性的充要条件，采用EM算法对参数进行条件极大似然估计并模拟仿真了估计量的性能，最后将模型应用于一组实例数据。

关键词: 整数值时间序列, 混合模型, INGARCH模型, 平稳性, 遍历性

Abstract:

Integer-valued time series with finite range are commonly encountered in practice, and many time series exhibit multimodality features on marginal or conditional distributions. However, most integer-valued models assume that the series is driven by a unimodal innovation sequence. Mixture models often perform well on data with multimodality and overdispersion features. A mixture model is considered for finite range integer-valued time series. In particalar, a binomial mixture integer-valued GARCH (B-MINGARCH) model is established, which includes a kind of binomial mixture ARCH (B-MINARCH) model with strict stationary and ergodicity. The necessary and sufficient stationary conditions are derived for B-MINGARCH achieving on- and two-order stability. The performances of the conditional maximum likelihood estimators via the EM algorithm are simulated. A real data example is also given.

Key words: integer-valued time series, mixture model, INGARCH model, stationarity, ergodicity

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