  The nearby red giant Aldebaran is known to host a gas giant planetary
companion from decades of ground-based spectroscopic radial velocity
measurements. Using Gaussian Process-based Continuous Auto-Regressive Moving
Average (CARMA) models, we show that these historic data also contain evidence
of acoustic oscillations in the star itself, and verify this result with
further dedicated ground-based spectroscopy and space-based photometry with the
Kepler Space Telescope. From the frequency of these oscillations we determine
the mass of Aldebaran to be $1.16 \pm 0.07 \, M_\odot$, and note that this
implies its planet will have been subject to insolation comparable to the Earth
for some of the star's main sequence lifetime. Our approach to sparse,
irregularly sampled time series astronomical observations has the potential to
unlock asteroseismic measurements for thousands of stars in archival data, and
push to lower-mass planets around red giant stars.
