Before revision:   Our quasi-likelihood is based on a central limit theorem for the realized volatility estimation error and a Whittle-type approximation to the auto-covariance of the log-volatility process.
After revision:  We construct a quasi-likelihood estimator and apply it to realized volatility time series. Our quasi-likelihood is based on a central limit theorem for the realized volatility estimation error and a Whittle-type approximation to the auto-covariance of the log-volatility process.