Quantile Regression Estimation for Poisson Autoregressive Models
针对泊松自回归模型的分位数回归估计难题，提出一种抖动平滑和变换策略，转化为连续型回归问题，并推导渐近理论，应用于股票交易量数据。
ABSTRACT 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 ‐step prediction method (‐QRF) is developed to forecast the ‐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.