Quadratic variations and estimation of the hurst index of the solution of SDE driven by a fractional Brownian motion

Maximum likelihood estimators of a long-memory process from discrete observations

“…Moreover, using the same argument of Kubilius and Melichov [43], we find that the estimatorĤ (defined by (10)) is a strong consistent estimator of H as N goes to infinity. Essentially, the problem of estimating the Hurst parameter in fractional processes has been extensively studied (see Shen et al [44]; Kubilius and Mishura [45]; Salomónab and Fortc [46]).…”

“…First, let us discuss the estimation of the Hurst parameter in the model (9). From Corollary 2 in Kubilius and Melichov [43], we immediately obtain the estimator of H from the observation Y:…”

Estimation of parameters of SDE driven by fractional Brownian motion with polynomial drift

“…For the first time, to our knowledge, an estimator of the Hurst parameter of a pathwise solution of a linear SDE driven by a fBm and its asymptotical behaviour were considered in [4]. A more general situation was considered in [10] using a different approach. Estimators for the Hurst parameter were constructed making use of the first and second order quadratic variations of the observed values of the solution.…”

On the convergence rates of Gladyshev’s Hurst index estimator

“…In 2005, A. Bégyn [3,4] considered the second order quadratic variations for processes with Gaussian increments. In 2008-2010, K. Kubilius and D. Melichov [7][8][9][10] studied the behavior of the first and second order quadratic variations of the pathwise solution of certain stochastic differential equations driven by fBm. It was shown that the quadratic variation based estimators remain strongly consistent in that case as well.…”