The renewable energy resources such as wind power have recently attracted more researchers’ attention. It is mainly due to the aggressive energy consumption, high pollution and cost of fossil fuels. In this era, the future fluctuations of these time series should be predicted to increase the reliability of the power network. In this paper, the dynamic characteristics and short-term predictability of hourly wind speed and power time series are investigated via nonlinear time series analysis methods such as power spectral density analysis, time series histogram, phase space reconstruction, the slope of integral sums, the method, the recurrence plot and the recurrence quantification analysis. Moreover, the interactive behavior of the wind speed and wind power time series is studied via the cross correlation, the cross and joint recurrence plots as well as the cross and joint recurrence quantification analyses. The results imply stochastic nature of these time series. Besides, a measure of the short-term mimic predictability of the wind speed and the underlying wind power has been derived for the experimental data of Spain’s wind farm.