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中文摘要：
为了解决厚尾分布不拥有完整的中心矩集合而无法进行矩估计的问题,在金融领域引入近年来在水文领域发展较为迅速的L-矩理论。在考虑当前预期和波动性条件下,基于L-矩理论分别考察了广义帕累托分布对高频收益超额数的静态尾部拟合和动态尾部拟合,应用条件VaR以及Kupiec-LR检验对拟合的结果进行了检验。研究结果表明,L-矩理论可以很好地解决厚尾分布的矩估计问题;VaR以及Kupiec-LR检验表明,基于L-矩的广义帕累托分布较好地拟合了极端条件下的收益率尾部,可以捕获极端条件下收益率时间序列动态特征。
英文摘要：
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.
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