  The CARMENES instrument is searching for periodic radial-velocity (RV)
variations of M dwarfs, which are induced by orbiting planets. However, there
are other potential sources of such variations, including rotational modulation
caused by stellar activity. We aim to investigate four M dwarfs (Ross 318, YZ
CMi, TYC 3529-1437-1, and EV Lac) with different activity levels and spectral
sub-types. Our goal is to compare the periodicities seen in 22 activity
indicators and the stellar RVs, and to examine their stability over time. For
each star, we calculated GLS periodograms of pseudo-equivalent widths of
chromospheric lines, indices of photospheric bands, the differential line width
as a measure of the width of the average photospheric absorption line, the RV,
the chromatic index that describes the wavelength dependence of the RV, and CCF
parameters. We also calculated periodograms for subsets of the data and
compared our results to TESS photometry. We find the rotation periods of all
four stars to manifest themselves in the RV and photospheric indicators,
particularly the TiO~7050 index, whereas the chromospheric lines show clear
signals only at lower activity levels. For EV Lac and TYC 3529-1437-1, we find
episodes during which indicators vary with the rotation period, and episodes
during which they vary with half the rotation period, similarly to photometric
light curves. The changing periodicities reflect the evolution of stellar
activity features on the stellar surface. We therefore conclude that our
results not only emphasise the importance of carefully analysing indicators
complementary to the RV in RV surveys, but they also suggest that it is also
useful to search for signals in activity indicators in subsets of the dataset,
because an activity signal that is present in the RV may not be visible in the
activity indicators all the time, in particular for the most active stars.
