Extreme quantile estimation under serial dependence

This paper evaluates the finite-sample performances of six extreme quantile estimators in the heavy-tailed series under serial dependence. Through Monte Carlo simulations, we show that the performances of the estimators are related to the degree of the serial dependence and the linearity/nonlinearity of the serial dependence. The maximum likelihood estimator based on the sliding block maxima is optimal to handle the linear serial dependence in data. The probability-weighted moment estimators are likely to be distorted by strong linear serial dependence. When the serial dependence is nonlinear, the excess kurtosis would affect the quantile estimation. The Weissman estimator outperforms when data has nonlinear serial dependence and a low excess kurtosis. The probability-weighted moment estimators based on the disjoint blocks is preferable when the data has a relatively high excess kurtosis. Additionally, this paper investigates an approach to improve the maximum likelihood estimators based on the block maxima in the GARCH models.