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.

Automated summary

This paper introduces a quantile regression estimation method for first-order integer-valued autoregressive models by defining a smoothing process, and derives estimators for the autoregressive coefficient and quantile of innovations using jittering method. The consistency and asymptotic normality of the estimators are established, and their performance is evaluated through Monte Carlo simulations, showing good performance in both simulations and real data applications.