Quantile Regression Estimation for Poisson Autoregressive Models

Estimating conditional quantiles plays a crucial role in modern risk management and other various applications. However, the quantile regression (QR) estimation of Poisson autoregressive (PAR) models, count-type models, remain an unresolved challenge. In this study, we propose a novel approach that employs a jittering smoothing method and a novel transformation strategy to convert this complex problem into an easily implementable quantile regression problem for continuous-type regression models. The asymptotic theory of the estimator is derived under some regularity conditions and the applications to four popular and classical PAR models are considered. Additionally, a novel (Formula presented.) -step prediction method ((Formula presented.) -QRF) is developed to forecast the (Formula presented.) -step conditional distribution. The finite sample performance of the method is examined, and its advantages over existing methods are illustrated by simulation studies and an empirical application to the daily stock volume dataset of Technofirst.