Consistent estimation for fractional stochastic volatility model under high‐frequency asymptotics
Consistent estimation for fractional stochastic volatility model under high‐frequency asymptotics
复制标题
高频渐近下分数随机波动率模型的一致性估计
DOI：
10.1111/mafi.12354
复制
发表时间：
2022
影响因子：
1.6
通讯作者：
and Westphal Rebecca
中科院分区：
文献类型：
--
作者：
Fukasawa Masaaki;Takabatake Tetsuya;and Westphal Rebecca
我们建立了一个连续时间近似对数正态分数随机波动模型的统计理论，以检验波动是否粗糙，即Hurst参数是否小于二分之一。我们构造了一个拟似然估计量，并将其应用于已实现的波动时间序列。我们的拟似然基于已实现波动率的误差分布和对数波动率过程的自协方差的惠特尔近似。我们证明了该估计器在高频渐近条件下的一致性，并通过仿真检验了它的有限样本性能。我们的实证研究表明，所检验的时间序列的波动性确实是粗糙的。
We develop a statistical theory for a continuous time approximately log‐normal fractional stochastic volatility model to examine whether the volatility is rough, that is, whether the Hurst parameter is less than one half. We construct a quasi‐likelihood estimator and apply it to realized volatility time series. Our quasi‐likelihood is based on the error distribution of the realized volatility and a Whittle‐type approximation to the auto‐covariance of the log‐volatility process. We prove the consistency of our estimator under high‐frequency asymptotics, and examine by simulations its finite sample performance. Our empirical study suggests that the volatility of the time series examined is indeed rough.