Liu Zhengwei, Zhu Fukang
School of Mathematics, Jilin University, 2699 Qianjin Street, Changchun 130012, China.
Entropy (Basel). 2020 Dec 31;23(1):62. doi: 10.3390/e23010062.
The thinning operators play an important role in the analysis of integer-valued autoregressive models, and the most widely used is the binomial thinning. Inspired by the theory about extended Pascal triangles, a new thinning operator named extended binomial is introduced, which is a general case of the binomial thinning. Compared to the binomial thinning operator, the extended binomial thinning operator has two parameters and is more flexible in modeling. Based on the proposed operator, a new integer-valued autoregressive model is introduced, which can accurately and flexibly capture the dispersed features of counting time series. Two-step conditional least squares (CLS) estimation is investigated for the innovation-free case and the conditional maximum likelihood estimation is also discussed. We have also obtained the asymptotic property of the two-step CLS estimator. Finally, three overdispersed or underdispersed real data sets are considered to illustrate a superior performance of the proposed model.
稀疏算子在整值自回归模型分析中起着重要作用，其中应用最广泛的是二项式稀疏。受扩展帕斯卡三角形理论的启发，引入了一种名为扩展二项式的新稀疏算子，它是二项式稀疏的一般情况。与二项式稀疏算子相比，扩展二项式稀疏算子有两个参数，在建模中更灵活。基于所提出的算子，引入了一种新的整值自回归模型，该模型能够准确且灵活地捕捉计数时间序列的离散特征。研究了无创新情况下的两步条件最小二乘（CLS）估计，并讨论了条件最大似然估计。我们还得到了两步CLS估计量的渐近性质。最后，考虑了三个过度分散或欠分散的真实数据集，以说明所提出模型的优越性能。
