Extreme Quantile Estimation for Autoregressive Models
针对自回归模型中极端尾部条件分位数估计不稳定的问题，基于极值理论提出新估计量，建立自回归系数与条件分位数函数的二阶条件联系，并证明渐近性质，通过模拟和美国汽油价格数据验证效果。
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.