To solve moment estimation problems in heavy-tailed distribution which do not possess set of finite central moments, we introduce the theory of L-moments which is developed in hydrology. Considering the factors of anticipation and volatility and fitting the tail with Generalized Pareto Distribution using high frequency excess return in the static and dynamic condition, we check the results by invoking Kupiec-LR and dynamic quantile test. The analysis of models and VaR shows that problems of moment estimation in heavy-tailed distribution can be solved with L-moments. Generalized Pareto Distribution is better fitted with the feature of return series in extreme condition, which has the implication that our model can catch the dynamic character of return series in extreme conditions.
庄泓刚, 王春峰, 房振明, 卢涛. 基于L-矩的厚尾分布动态拟合研究[J]. J4, 2010, 7(8): 1254-.
ZHUANG Hong-Gang, WANG Chun-Feng, FANG Zhen-Ming, LU Tao. A Dynamic Fitting Model of Heavy-Tailed Distribution Based on L-Moments. J4, 2010, 7(8): 1254-.