This paper proposes a novel conditional heteroscedastic time series model by applying the framework of quantile regression processes to the ARCH(\infty) 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 (CQR) 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.

翻译：本文通过将分位数回归过程框架应用于GARCH模型的ARCH(∞)形式，提出了一种新颖的条件异方差时间序列模型。该模型能够为时间序列在不同分位水平上的条件分位数提供变化结构，同时将常用的GARCH模型作为特例包含在内。讨论了模型的严格平稳性。为增强对厚尾分布的稳健性，提出了一种自加权分位数回归估计量。在中间分位水平上，分位数回归表现令人满意，但由于数据稀疏性，其在高分位水平上的精度会下降。为解决此问题，进一步引入了一种自加权复合分位数回归估计量，并基于一个采用灵活Tukey-lambda分布描述新息项的近似GARCH模型，我们能够通过借用中间分位水平的信息来外推高分位水平。建立了所提估计量的渐近性质。通过模拟实验评估了所提方法的有限样本表现，并给出了一个实证示例以说明新模型的有效性。