In this paper, we develop a generalized method of moments approach for joint estimation of the parameters of a fractional log-normal stochastic volatility model. We show that with an arbitrary Hurst exponent an estimator based on integrated variance is consistent. Moreover, under stronger conditions we also derive a central limit theorem. These results stand even when integrated variance is replaced with a realized measure of volatility calculated from discrete high-frequency data. However, in practice a realized estimator contains sampling error, the effect of which is to skew the fractal coefficient toward "roughness". We construct an analytical approach to control this error. In a simulation study, we demonstrate convincing small sample properties of our approach based both on integrated and realized variance over the entire memory spectrum. We show that the bias correction attenuates any systematic deviance in the estimated parameters. Our procedure is applied to empirical high-frequency data from numerous leading equity indexes. With our robust approach the Hurst index is estimated around 0.05, confirming roughness in integrated variance.

翻译：在本文中,我们开发了一种通用的瞬间方法,用于共同估计分数正正态随机挥发性模型的参数。 我们用任意的赫斯特显示一个基于集成差异的估测符是一致的。 此外,在更强的条件下,我们还得出了一个中央限值。 这些结果即使综合差异被从离散高频数据计算出来的已实现的挥发性测量值所取代。 然而,在实践上,一个已实现的测算器包含抽样错误,其结果是将折射系数扭曲到“粗度 ” 。 我们构建了一个分析方法来控制这个错误。 在模拟研究中,我们展示了基于整个记忆范围的综合和已实现差异的我们方法的微小样本特性。 我们显示,偏差校正使估计参数中的任何系统性偏差有所减弱。 我们的程序适用于许多主要公平指数中的经验性高频度数据。 我们的稳健方法估计赫斯特指数约为0.05, 证实了整体差异中的粗度。