Many financial time series have varying structures at different quantile levels, and also exhibit the phenomenon of conditional heteroskedasticity at the same time. However, there is presently no time series model that accommodates both of these features. This paper fills the gap by proposing a novel conditional heteroskedastic model called “quantile double autoregression”. The strict stationarity of the new model is derived, and self-weighted conditional quantile estimation is suggested. Two promising properties of the original double autoregressive model are shown to be preserved. Based on the quantile autocorrelation function and self-weighting concept, three portmanteau tests are constructed to check the adequacy of the fitted conditional quantiles. The finite sample performance of the proposed inferential tools is examined by simulation studies, and the need for use of the new model is further demonstrated by analyzing the S&P500 Index.

许多金融时间序列在不同的分位数水平上具有不同的结构，同时还表现出条件异方差现象。然而，目前还没有能够同时满足这两个特征的时间序列模型。本文通过提出一种称为“分位数双自回归”的新条件异方差模型来填补这一空白。推导了新模型的严格平稳性，提出了自加权条件分位数估计。显示保留了原始双自回归模型的两个有希望的特性。基于分位数自相关函数和自加权概念，构建了三个portmanteau检验来检查拟合条件分位数的充分性。