Quantile autoregressive conditional heteroscedasticity

• 成果类型: Article
• 署名作者: Zhu, Qianqian; Tan, Songhua; Zheng, Yao; Li, Guodong
• 署名单位: Shanghai University of Finance & Economics; University of Connecticut; University of Hong Kong
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkad068
• 发表日期: 2023
• 页码: 1099-1127
• 关键词: mixing properties; regression; models; inference; RISK; ARCH; estimators; variance

摘要

This article proposes a novel conditional heteroscedastic time series model by applying the framework of quantile regression processes to the ARCH(& INFIN;) form of the GARCH model. This model can provide varying structures for conditional quantiles of the time series across different quantile levels, while including the commonly used GARCH model as a special case. The strict stationarity of the model is discussed. For robustness against heavy-tailed distributions, a self-weighted quantile regression (QR) estimator is proposed. While QR performs satisfactorily at intermediate quantile levels, its accuracy deteriorates at high quantile levels due to data scarcity. As a remedy, a self-weighted composite quantile regression estimator is further introduced and, based on an approximate GARCH model with a flexible Tukey-lambda distribution for the innovations, we can extrapolate the high quantile levels by borrowing information from intermediate ones. Asymptotic properties for the proposed estimators are established. Simulation experiments are carried out to access the finite sample performance of the proposed methods, and an empirical example is presented to illustrate the usefulness of the new model.