Time-Varying High Quantile Estimation for Nonstationary Tail Dependent Time Series

原文摘要

We consider the problem of time-varying high quantile estimation for a general class of nonstationary tail dependent time series. Unlike the conventional quantile analysis in which the quantile level is typically assumed to be fixed, the current high quantile setting requires the quantile level to grow with the sample size to capture the tail phenomenon. In addition, for nonstationary time series data, the underlying data generating mechanism is expected to change over time, and as a result the associated time-varying high quantile can no longer be treated as a constant parameter making existing results not directly applicable. In this article, we model the underlying time-varying high quantile as a nonparametric function of time to avoid any parametric misspecification, and we establish the consistency and central limit theorem of nonparametric high quantile estimators for a general class of nonstationary tail dependent time series. It can be seen from our limit theorems that the asymptotic behavior of nonparametric high quantile estimators can be affected by both the double asymptotic scheme caused by the growing quantile level and the serial tail dependence in time series data. Numerical results are provided to illustrate the developed results, and an extension to time-varying high quantile regression models is also discussed.

摘要来源：OpenAlex