GPIGINAR(1)模型的贝叶斯估计
Bayesian Estimation of the GPIGINAR(1) Model
DOI: 10.12677/sa.2025.144117, PDF,    科研立项经费支持
作者: 李 平, 卢飞龙*：辽宁科技大学理学院，辽宁 鞍山
关键词: GPIGINAR(1)模型；贝叶斯估计；MCMC算法；GPIGINAR(1) Model； Bayesian Estimation； MCMC Algorithm
摘要: 当前研究表明，整数值时间序列通常呈现出重尾特征。然而，能够处理这类具有重尾特征数据的模型相对较少。本文聚焦于广义泊松逆高斯INAR(1) (GPIGINAR(1))模型，该模型能够拟合重尾特征。文中采用自适应马尔可夫链蒙特卡洛(MCMC)算法，对该模型中所关注的参数进行贝叶斯估计，并将其结果与极大似然估计结果进行对比，以此证明所提方法的有效性。最后，通过具体实例进一步说明该模型在处理此类数据时的有效性，以及该算法在解决这类问题时的可行性。
Abstract: Current research shows that integer-valued time series usually exhibit heavy-tailed characteristics. However, relatively few models are capable of handling data with such heavy-tailed characteristics. This paper focuses on the Generalized Poisson Inverse Gaussian INAR(1) (GPIGINAR(1)) model, which is able to fit heavy-tailed features. In this paper, the Adaptive Markov Chain Monte Carlo (MCMC) algorithm is adopted to perform Bayesian estimation on the parameters of interest in this model. The results are then compared with those of maximum likelihood estimation to prove the effectiveness of the proposed method. Finally, specific examples are used to further illustrate the effectiveness of this model in processing such data and the feasibility of the algorithm in solving such problems.
文章引用：李平, 卢飞龙. GPIGINAR(1)模型的贝叶斯估计[J]. 统计学与应用, 2025, 14(4): 369-382. https://doi.org/10.12677/sa.2025.144117

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