Huang Jie, Zhu Fukang
School of Mathematics, Jilin University, 2699 Qianjin Street, Changchun 130012, China.
Entropy (Basel). 2021 Jun 4;23(6):713. doi: 10.3390/e23060713.
A Poisson distribution is commonly used as the innovation distribution for integer-valued autoregressive models, but its mean is equal to its variance, which limits flexibility, so a flexible, one-parameter, infinitely divisible Bell distribution may be a good alternative. In addition, for a parameter with a small value, the Bell distribution approaches the Poisson distribution. In this paper, we introduce a new first-order, non-negative, integer-valued autoregressive model with Bell innovations based on the binomial thinning operator. Compared with other models, the new model is not only simple but also particularly suitable for time series of counts exhibiting overdispersion. Some properties of the model are established here, such as the mean, variance, joint distribution functions, and multi-step-ahead conditional measures. Conditional least squares, Yule-Walker, and conditional maximum likelihood are used for estimating the parameters. Some simulation results are presented to access these estimates' performances. Real data examples are provided.
泊松分布通常用作整数值自回归模型的创新分布，但其均值等于方差，这限制了灵活性，因此灵活的单参数无限可分贝分布可能是一个很好的替代方案。此外，对于较小值的参数，贝分布接近泊松分布。在本文中，我们基于二项式稀疏算子引入了一种新的一阶非负整数值自回归模型，该模型具有贝创新。与其他模型相比，新模型不仅简单，而且特别适用于呈现过度分散的计数时间序列。这里建立了模型的一些性质，如均值、方差、联合分布函数和多步超前条件测度。使用条件最小二乘法、尤尔-沃克法和条件最大似然法来估计参数。给出了一些模拟结果以评估这些估计的性能。提供了实际数据示例。
