重尾估计在金融数据中的应用

Application of the Heavy-tailed Estimation in Financial Data

重尾分布是存在于许多高频时间序列的边缘分布,而且在尾部存在着大量的信息。基于重尾分布尾指数估计的Hill估计方法提出优化改进的AvHill估计方法,该方法成功地降低了Hill估计的方差。同时,融合矩估计方法和最大似然估计方法的思想,给出重尾评测的MM估计,其在渐近方差上也低于Hill估计。基于理论仿真随机获取的1000个数据进行评测方法的比较分析,Hill估计、AvHill估计和MM估计在的测试中表现了各个估计的稳定程度并在不同的数据容量中表现出了不同的优点。针对股票数据的涨跌绝对值的测试中,将3种方法进行综合运用估计,通过对3种估计方法的交点进行数据上的分段,可发现各种估计方法在不同的数据容量中的优缺点以及各种估计方法的优缺点。

There exist many marginal distributions of high frequency time series data in the Heavy-tailed distribution which stores a great deal of information in its tail. Based on the Hill's estimator which is the classic in the Heavy-tailed index, the AvHill's estimator is proposed and AvHill's estimator successfully reduce the variance of the Hill's estimator. The MM estimator is proposed which is based on the moment estimator and the maximum likelihood meanwhile and it also reduces the variance of the Hill's estimator. Based on the theoretical simulation in the 1000 data and compare the data, Hill's estimator , AvHill's estimator and MM estimator express their own advantage in the different data capacity and degree of stability. We use Hill's estimator , AvHill's estimator and MM estimator to estimate the absolute value in the up and down of the stock data. We find the data segment using the intersections of the curves of the three estimators to reflects the function and the advantage of the three estimator in the different data segment.