Quantile Regression for Thinning-based INAR(1) Models of Time Series of Counts

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.