We consider here wind speed time series and the aggregate output wind power from a wind farm. We study their scaling statistics in the framework of fully developed turbulence and Kolmogorov's theory. We estimate their Fourier power spectra and consider their scaling properties in the physical space. We show that the atmospheric wind speed and the aggregate power output from a wind farm are intermittent and multifractal over a wide range of scales. The coupling between simultaneous data of the wind speed and aggregate power output is investigated through a joint multifractal description using the generalized correlation functions (GCFs). This multiscaling test is compatible with a linear relation between the wind speed and the aggregate power output fluctuations for timescales T ⩾ 103 s ≃ 15 min.