ABSTRACT

A quantile autoregresive model is a useful extension of classical autoregresive models as it can capture the influences of conditioning variables on the location, scale, and shape of the response distribution. However, at the extreme tails, standard quantile autoregression estimator is often unstable due to data sparsity. In this article, assuming quantile autoregresive models, we develop a new estimator for extreme conditional quantiles of time series data based on extreme value theory. We build the connection between the second-order conditions for the autoregression coefficients and for the conditional quantile functions, and establish the asymptotic properties of the proposed estimator. The finite sample performance of the proposed method is illustrated through a simulation study and the analysis of U.S. retail gasoline price.

摘要

分位数自回归模型是经典自回归模型的有用扩展，因为它可以捕获条件变量对响应分布的位置，规模和形状的影响。但是，由于数据稀疏性，标准的分位数自回归估计器经常处于不稳定状态。在本文中，假设使用分位数自回归模型，我们将基于极值理论为时间序列数据的极端条件分位数开发一种新的估计器。我们建立了自回归系数和条件分位数函数的二阶条件之间的联系，并建立了所提出估计量的渐近性质。通过仿真研究和对美国汽油零售价格的分析，说明了该方法的有限样本性能。