A Flexible Model for Time Series of Counts with Overdispersion or Underdispersion, Zero-Inflation and Heavy-Tailedness
A Flexible Model for Time Series of Counts with Overdispersion or Underdispersion, Zero-Inflation and Heavy-Tailedness
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DOI：
10.1007/s40304-022-00327-1
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发表时间：
2023-03
影响因子：
0.9
通讯作者：
Lianyong Qian;Fukang Zhu
中科院分区：
文献类型：
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作者：
Lianyong Qian;Fukang Zhu
在实践中观察到的计数时间序列往往表现出过度分散或欠分散，零膨胀，甚至重尾（尾部概率不可忽略或下降非常缓慢）。本文提出了一种基于广义Conway-Maxwell-Poisson分布的更灵活的整数值GARCH模型来建模计数时间序列，为处理过分散或欠分散、零膨胀和重尾计数时间序列提供了一个统一的框架。该分布通过添加一个参数来推广Conway-Maxwell-Poisson分布，该参数起着控制尾部长度的作用。我们研究所提出的模型的基本性质，并通过条件极大似然方法获得参数的估计。模拟和真实的数据的数值结果证实了所提出的模型的良好性能。
Time series of counts observed in practice often exhibit overdispersion or underdispersion, zero inflation and even heavy-tailedness (the tail probabilities are non-negligible or decrease very slowly). In this article, we propose a more flexible integer-valued GARCH model based on the generalized Conway–Maxwell–Poisson distribution to model time series of counts, which offers a unified framework to deal with overdispersed or underdispersed, zero-inflated and heavy-tailed time series of counts. This distribution generalizes the Conway–Maxwell–Poisson distribution by adding a parameter, which plays the role of controlling the length of the tail. We investigate basic properties of the proposed model and obtain estimators of parameters via the conditional maximum likelihood method. The numerical results with both simulated and real data confirm the good performance of the proposed model.