  The He I infrared (IR) triplet at 10830 \AA is known as an activity indicator
in solar-type stars and has become a primary diagnostic in exoplanetary
transmission spectroscopy. He I lines are a tracer of the stellar
extreme-ultraviolet irradiation from the transition region and corona. We study
the variability of the He I IR triplet lines in a spectral time series of 319
M~dwarf stars that was obtained with the CARMENES high-resolution optical and
near-infrared spectrograph at Calar Alto. We detect He I IR line variability in
18% of our sample stars, all of which show H$\alpha$ in emission. Therefore, we
find detectable He I IR variability in 78% of the sub-sample of stars with
H$\alpha$ emission. Detectable variability is strongly concentrated in the
latest spectral sub-types, where the He I IR lines during quiescence are
typically weak. The fraction of stars with detectable He I IR variation remains
lower than 10% for stars earlier than M3.0 V, while it exceeds 30% for the
later spectral sub-types. Flares are accompanied by particularly pronounced
line variations, including strongly broadened lines with red and blue
asymmetries. However, we also find evidence for enhanced He I IR absorption,
which is potentially associated with increased high-energy irradiation levels
at flare onset. Generally, He I IR and H$\alpha$ line variations tend to be
correlated, with H$\alpha$ being the most sensitive indicator in terms of
pseudo-equivalent width variation. This makes the He I IR triplet a favourable
target for planetary transmission spectroscopy.
