Temporal director fluctuations in nematic ordering were studied by computer simulation on the Lebwohl-Lasher model as well as by neutron-scattering experiments on the nematogen d-PAA. The time-series data have been analyzed by the rescaled-range method and in terms of the power spectrum in order to determine the Hurst exponent H. Theory and experiment are in good agreement. A value of H1 was found for the nematic phase, characterizing fractional Brownian motion, whereas H0.5, reflecting ordinary Brownian motion, applies in the isotropic phase. Field-induced crossover from fractional to ordinary Brownian motion was observed in the nematic phase.