Multiple and changing cycles of active stars

Context. Long-term observational data have information on the magnetic cycles of active stars and that of the Sun. The changes in the activity of our central star have basic effects on Earth, such as variations in the global climate, so that understanding the nature of these variations is extremely important. Aims. The observed variations related to magnetic activity cannot be treated as stationary periodic variations, therefore methods like Fourier transform or different versions of periodograms only give partial information on the nature of the light variability. We demonstrate that time-frequency distributions provide useful tools for analysing the observations of active stars. Methods. We tested and used different methods, such as short-term Fourier transform, wavelet, and generalised time-frequency distributions, for analysing temporal variations in timescales of observational data. Results. With test data we demonstrate that the observational noise has practically no effect on the determination in the long-term changes of time-series observations of active stars. The rotational signal may modify the determined cycles, therefore it is advisable to remove it from the data. Wavelets are less powerful in recovering complex long-term changes than other distributions that are discussed. By applying our technique to the sunspot data we find a complicated, multi-scale evolution in the solar activity