一种带有自权重的积分波动率的非参估计

摘要

A nonparametric estimator is proposed for the class of integrated cross volatilities of thernform 1∫0 f(xt)σ2tdt, where f is a continuous function, σ2s is the instantaneous cross volatility of continuousrnsemimartingale X. Using "Realized Volatility" , the asymptotic properties, which include consistency and asymptotic normality are obtained. A studentized version has been given and this can be used to construct confidence interval and do hypothesis testing.%为了对带有自权重的积分波动率∫f(X(t))σ2(t)dt进行估计,定义了一个新的非参数估计量,并利用“已实现”波动率的方法,证明了该估计量是积分∫10f(X(t))σ2dt的一致估计量,同时还得到此估计量的渐近正态分布以及学生化形式,从而可对该积分做区间估计或假设检验.