One-step estimation for the fractional Gaussian noise model at high-frequency.

Summary A new sequence of estimators is introduced to estimate the parameters of the fractional Gaussian noise at high-frequency. This sequence is defined by an initial sequence of quadratic generalized variations based estimators (QGV) and a single Fisher scoring step. It presents certain advantages over the sequence of maximum likelihood estima-tors (MLE) which is rate and variance efficient and the QGV which is only rate efficient. Indeed, it is much less computationally demanding than the MLE while keeping the efficient asymptotic variance. The local weak efficiency of crude oil markets is analyzed through likelihood-ratio hypothesis tests based on the joint estimation of the volatility and the Hurst exponent in the high-frequency scheme.