I'm in trouble finding the optimal estimator of the Hurst parameter in the fractional Brownian motion. Is there something better than the Whittle estimator?
Thanks in advance
I'm in trouble finding the optimal estimator of the Hurst parameter in the fractional Brownian motion. Is there something better than the Whittle estimator?
Thanks in advance
Call $(X_k)_{k\geqslant0}$ the values of the process observed at time intervals of length $T$. Ergodic estimators of $H$ based on the second moment are $ \widehat H_n=\frac{\log\left(\sum\limits_{k=1}^n(X_k-X_{k-1})^2\right)-\log n}{2\log T}. $ For a study of $\widehat H_n$ and some comparisons to other approaches, see New Estimation Techniques for Fractional Brownian Motion by V. Dobric, D. Scansaroli, R. Storer.