Before revision:  Motivated by this preliminary finding, we construct a quasi-likelihood estimator for a fractional stochastic volatility model and apply it to realized variance time series to examine whether the  volatility is really rough.
After revision:  Motivated by this preliminary finding, we construct a quasi-likelihood estimator for a fractional stochastic volatility model and apply it to realized variance time series to examine whether the Hurst parameter is indeed estimated smaller than half, that is, whether the volatility is really rough.