There exist many marginal distributions of high frequencytime series data in the Heavy-tailed distribution which stores a great deal of information inits tail. Based onthe Hill’s estimator which is the classic in the Heavy-tailed index

the AvHill’sestimator is proposed and AvHill’s estimator successfully reduce the varianceof the Hill’s estimator. The MM estimator is proposed which is based on the momentestimator and the maximum likelihood meanwhile and it also reduces the varianceof the Hill’s estimator. Based on the theoretical simulation in the 1000 data and comparethe data

Hill’s estimator

AvHill’s estimator and MM estimator express theirown advantage in the different data capacity and degree of stability. We useHill’s estimator

AvHill’s estimator and MM estimator to estimate the absolutevalue in the up and down of the stock data. We find the data segment usingthe intersections of the curves of the three estimators to reflects thefunction and the advantage of the three estimator in the different data segment.