  The optical light curves of many quasars show variations of tenths of a
magnitude or more on time scales of months to years. This variation often
cannot be described well by a simple deterministic model. We perform a Bayesian
comparison of over 20 deterministic and stochastic models on 6304 QSO light
curves in SDSS Stripe 82. We include the damped random walk (or
Ornstein-Uhlenbeck [OU] process), a particular type of stochastic model which
recent studies have focused on. Further models we consider are single and
double sinusoids, multiple OU processes, higher order continuous autoregressive
processes, and composite models. We find that only 29 out of 6304 QSO
lightcurves are described significantly better by a deterministic model than a
stochastic one. The OU process is an adequate description of the vast majority
of cases (6023). Indeed, the OU process is the best single model for 3462 light
curves, with the composite OU process/sinusoid model being the best in 1706
cases. The latter model is the dominant one for brighter/bluer QSOs.
Furthermore, a non-negligible fraction of QSO lightcurves show evidence that
not only the mean is stochastic but the variance is stochastic, too. Our
results confirm earlier work that QSO light curves can be described with a
stochastic model, but place this on a firmer footing, and further show that the
OU process is preferred over several other stochastic and deterministic models.
Of course, there may well exist yet better (deterministic or stochastic) models
which have not been considered here.
