估计员
赫斯特指数
已实现方差
数学
统计
随机波动
波动性(金融)
差异(会计)
计量经济学
经济
会计
作者
Anine E. Bolko,Kim Christensen,Mikko S. Pakkanen,Bezirgen Veliyev
出处
期刊:Cornell University - arXiv
日期:2020-10-09
被引量:1
摘要
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.
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