In the last years efforts have been made to determine parameters of stellar coronal
mass ejections (CMEs), on the one hand via acquiring dedicated observing time at telescopes
and on the other hand via searching data archives. Here we present a search for CMEs
on solar-like stars using optical spectroscopic data from the Polarbase and ESO HARPS
Phase 3 archives. For detecting stellar CMEs we use the signature of filaments/prominences
being ejected from a star, which is Doppler-shifted emission/absorption occurring
on the blue side of Balmer lines, as filaments/prominences are very pronounced in
Balmer lines. Using more than 3700 hours of on-source time of 425 stars we aim for
a statistical determination of CME parameters, such as projected velocity, occurrence
frequency, and mass. The target stars are nearby objects and consist of F-K main-sequence
stars of various ages. We find no signature of CME activity and a very low level of
flaring activity (10 out of 425 stars). Comparing this to results from the Kepler
mission, the fraction of flaring stars is more or less consistent. Comparing extrapolated
Hα flare rates to the sparse detection of flares reveals that we could have detected
more flares. We therefore determined the full-disk Hα signal of one of the strongest
solar flares in the last solar cycles. This showed that we would have needed data
with higher S/N to detect such a flare in our data. Finally, we compared the observed
upper limits of CME rates of our target stars to modelled CME rates. The modelled
CME rates are mostly below the observationally determined upper limits, indicating
that most on-source times per star were too short to detect stellar CMEs with this
method. The sparse detection of flares and the non-detection of CMEs may be explained
by biases naturally introduced by using archival data, as well as a a low level of
activity of the target stars. We conclude with a short report on ongoing and future
activities of the search for stellar CMEs.