High-quantile regression for tail-dependent time series
High-quantile regression for tail-dependent time series
复制标题
尾部相依时间序列的高分位数回归
DOI：
10.1093/biomet/asaa046
复制
发表时间：
2020-07
期刊：
影响因子：
2.7
通讯作者：
Ting Zhang
中科院分区：
文献类型：
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作者：
Ting Zhang
分位数回归是研究回归变量对响应分布分位数影响的一种流行而强大的方法。然而，现有的分位数回归的结果主要是在分位数水平固定的情况下发展的，并且数据通常被假设为独立的。最近的应用程序的动机，我们考虑的情况下，（i）的分位数水平是不固定的，可以随着样本量的增长，以捕捉尾部现象，和（ii）的数据不再是独立的，但收集的时间序列，可以表现出连续的依赖性在尾部和非尾部区域。为了研究时间序列中高分位数回归估计量的渐近理论，我们引入了一个尾对抗稳定性条件，这是以前没有描述过的，并表明它导致了一个可解释的和方便的框架，用于获得时间序列的极限定理，表现出序列依赖于尾区域，但不一定是强混合。数值实验进行说明尾部依赖高分位数回归估计的效果，简单地忽略尾部依赖可能会产生误导$p$值。
Quantile regression is a popular and powerful method for studying the effect of regressors on quantiles of a response distribution. However, existing results on quantile regression were mainly developed for cases in which the quantile level is fixed, and the data are often assumed to be independent. Motivated by recent applications, we consider the situation where (i) the quantile level is not fixed and can grow with the sample size to capture the tail phenomena, and (ii) the data are no longer independent, but collected as a time series that can exhibit serial dependence in both tail and non-tail regions. To study the asymptotic theory for high-quantile regression estimators in the time series setting, we introduce a tail adversarial stability condition, which had not previously been described, and show that it leads to an interpretable and convenient framework for obtaining limit theorems for time series that exhibit serial dependence in the tail region, but are not necessarily strongly mixing. Numerical experiments are conducted to illustrate the effect of tail dependence on high-quantile regression estimators, for which simply ignoring the tail dependence may yield misleading $p$-values.