In this study, we investigate the global ionospheric impact of high‐speed solar wind streams/corotating interaction regions (HSS/CIR). A series of 10 such events are identified between December 1, 2007 and April 29, 2008, characterized in the frequency domain by the main spectral peaks corresponding to 27, 13.5, 9, and 6.75 days. The spectra of solar wind magnetic field, speed, and proton density, as well as those of the geomagnetic indices AE and SYM‐H, are solely dominated by these features. By contrast, the ionospheric NmF2 and to a lesser extent the hmF2 spectra have a much more complex structure, with secondary peaks adding to or replacing the main ones. We argue that this is evidence of the nonlinear nature of the magnetosphere‐ionosphere coupling, highlighted particularly in the NmF2 ionospheric response. Additionally, we show that hmF2 is more closely correlated than NmF2 to all parameters describing the solar wind and geomagnetic activity. Finally, the ionospheric response shows a higher correlation with Bz than any other solar wind parameter, and higher with SYM‐H than AE, indicating that for the low‐frequency part of the spectrum, high‐latitude Joule heating and particle precipitation play a secondary role to that of prompt penetration electric fields in dictating the ionospheric response to geomagnetic activity, in the case of this sequence of HSS/CIR events.