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。该模型能够为不同分位点水平下的时间序列条件分位数提供可变结构，同时将常用的GARCH模型作为特例包含在内。本文讨论了模型的严格平稳性。针对厚尾分布的稳健性问题，提出了一种自加权分位数回归（QR）估计量。尽管QR在中间分位点水平表现令人满意，但由于数据稀缺，其在高分位点水平的准确性会降低。为此，进一步引入自加权复合分位数回归（CQR）估计量，并基于具有灵活Tukey-lambda分布新息项的近似GARCH模型，通过借调中间分位点的信息实现对高分位点水平的外推。建立了所提估计量的渐近性质。通过仿真实验评估所提方法的有限样本性能，并通过实证案例展示新模型的实用性。