  I introduce a general, Bayesian method for modelling univariate time series
data assumed to be drawn from a continuous, stochastic process. The method
accommodates arbitrary temporal sampling, and takes into account measurement
uncertainties for arbitrary error models (not just Gaussian) on both the time
and signal variables. Any model for the deterministic component of the
variation of the signal with time is supported, as is any model of the
stochastic component on the signal and time variables. Models illustrated here
are constant and sinusoidal models for the signal mean combined with a Gaussian
stochastic component, as well as a purely stochastic model, the
Ornstein-Uhlenbeck process. The posterior probability distribution over model
parameters is determined via Monte Carlo sampling. Models are compared using
the "cross-validation likelihood", in which the posterior-averaged likelihood
for different partitions of the data are combined. In principle this is more
robust to changes in the prior than is the evidence (the prior-averaged
likelihood). The method is demonstrated by applying it to the light curves of
11 ultra cool dwarf stars, claimed by a previous study to show statistically
significant variability. This is reassessed here by calculating the
cross-validation likelihood for various time series models, including a null
hypothesis of no variability beyond the error bars. 10 of 11 light curves are
confirmed as being significantly variable, and one of these seems to be
periodic, with two plausible periods identified. Another object is best
described by the Ornstein-Uhlenbeck process, a conclusion which is obviously
limited to the set of models actually tested.
