  The time-variable velocity fields of solar-type stars limit the precision of
radial-velocity determinations of their planets' masses, obstructing detection
of Earth twins. Since 2015 July we have been monitoring disc-integrated
sunlight in daytime using a purpose-built solar telescope and fibre feed to the
HARPS-N stellar radial-velocity spectrometer. We present and analyse the solar
radial-velocity measurements and cross-correlation function (CCF) parameters
obtained in the first 3 years of observation, interpreting them in the context
of spatially-resolved solar observations. We describe a Bayesian mixture-model
approach to automated data-quality monitoring. We provide dynamical and daily
differential-extinction corrections to place the radial velocities in the
heliocentric reference frame, and the CCF shape parameters in the sidereal
frame. We achieve a photon-noise limited radial-velocity precision better than
0.43 m s$^{-1}$ per 5-minute observation. The day-to-day precision is limited
by zero-point calibration uncertainty with an RMS scatter of about 0.4 m
s$^{-1}$. We find significant signals from granulation and solar activity.
Within a day, granulation noise dominates, with an amplitude of about 0.4 m
s$^{-1}$ and an autocorrelation half-life of 15 minutes. On longer timescales,
activity dominates. Sunspot groups broaden the CCF as they cross the solar
disc. Facular regions temporarily reduce the intrinsic asymmetry of the CCF.
The radial-velocity increase that accompanies an active-region passage has a
typical amplitude of 5 m s$^{-1}$ and is correlated with the line asymmetry,
but leads it by 3 days. Spectral line-shape variability thus shows promise as a
proxy for recovering the true radial velocity.
