  In this article, we consider the problem of estimating fractional processes
based on noisy high-frequency data. Generalizing the idea of pre-averaging to a
fractional setting, we exhibit a sequence of consistent estimators for the
unknown parameters of interest by proving a law of large numbers for associated
variation functionals. In contrast to the semimartingale setting, the optimal
window size for pre-averaging depends on the unknown roughness parameter of the
underlying process. We evaluate the performance of our estimators in a
simulation study and use them to empirically verify Kolmogorov's 2/3-law in
turbulence data contaminated by instrument noise.
