Detection and Estimation of Outliers in the Empirical Likelihood INAR(1) Model

整值时间序列可出现在教育，金融，医疗，交通等诸多领域，本文旨在研究利用经验似然方法对整值时间序列中的加性离群点与新息离群点进行检测与估计，并针对凸包问题进行了详细讨论，最后通过数值模拟充分验证了经验似然方法检测离群点的有效性。仿真实验结果表明，经验似然方法可以有效检测与估计出不同新息分布下一阶整值时间序列模型中的离群点。Integer-valued time series can appear in various fields such as education, finance, healthcare, and transportation. This paper aims to investigate the detection and estimation of additive outliers and innovation outliers in integer-valued time series based on the empirical likelihood method. Additionally, the convex hull problem is discussed in detail. Finally, numerical simulations are conducted to fully verify the effectiveness of the empirical likelihood method in detecting outliers. The simulation results show that the empirical likelihood method can effectively detect and estimate outliers in first-order integer-valued time series models with different innovation distributions.