In this paper, we develop the quantile regression (QR) estimation for the first-order integer-valued autoregressive (INAR(1)) models by defining the smoothing INAR(1) process. Jittering method is used to derive the QR estimators for the autoregressive coefficient and the quantile of innovations. The consistency and asymptotic normality of the proposed estimators are established. The performances of the proposed estimation procedures are evaluated by Monte Carlo simulations. The results show that the proposed procedures perform well for simulations and a real data application.

中文翻译：

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基于细化的计数时间序列的INAR（1）模型的分位数回归

在本文中，我们通过定义平滑的INAR（1）过程，为一阶整数值自回归（INAR（1））模型开发了分位数回归（QR）估计。抖动方法用于推导自回归系数和创新分位数的QR估计量。建立了所提出估计量的一致性和渐近正态性。提出的估计程序的性能通过蒙特卡洛模拟进行评估。结果表明，所提出的程序在仿真和实际数据应用中表现良好。