基于负二项稀疏算子和推广的负二项稀疏算子的INAR(1)模型的比较

Comparison of INAR(1)Models Based on Negative Binomial Thinning Operators and Extended Negative Binomial Thinning Operators

本文利用条件极大似然估计的方法比较利用预设新息分布法基于推广的负二项稀疏算子INAR(1)模型和负二项稀疏算子的INAR(1)模型的参数估计情况。通过对取不同新息项分布的两个模型分别进行数值模拟,并对两个模型数值模拟的结果进行对比来直观地表明由于基于负二项稀疏算子的INAR(1)模型在x=0点时概率质量不存在进而模型的所有边际分布不存在,从而证明利用预设新息分布法基于负二项稀疏算子的INAR(1)模型不存在,也表明推广的负二项稀疏算子在利用预设新息分布法构建INAR(1)模型中的必要性。

This article uses the method of conditional maximum likelihood estimation to compare the parameter estimation of the INAR(1)model based on the generalized negative binomial thinning operator and the INAR(1)model using the preset innovation distribution method.By conducting numerical simulations on two models with different distribution of innovation terms and comparing the numerical simulation results of the two models,it is intuitively shown that the INAR(1)model based on negative binomial thinning operator does not have a probability mass at point x=0,and therefore all edge distributions of the model do not exist.This proves that the INAR(1)model based on negative binomial thinning operator using the preset innovation distribution method does not exist,This also indicates the necessity of the generalized negative binomial thinning operator in constructing the INAR(1)model using the preset innovation distribution method.