  We present the use of continuous-time autoregressive moving average (CARMA)
models as a method for estimating the variability features of a light curve,
and in particular its power spectral density (PSD). CARMA models fully account
for irregular sampling and measurement errors, making them valuable for
quantifying variability, forecasting and interpolating light curves, and for
variability-based classification. We show that the PSD of a CARMA model can be
expressed as a sum of Lorentzian functions, which makes them extremely flexible
and able to model a broad range of PSDs. We present the likelihood function for
light curves sampled from CARMA processes, placing them on a statistically
rigorous foundation, and we present a Bayesian method to infer the probability
distribution of the PSD given the measured lightcurve. Because calculation of
the likelihood function scales linearly with the number of data points, CARMA
modeling scales to current and future massive time-domain data sets. We
conclude by applying our CARMA modeling approach to light curves for an X-ray
binary, two AGN, a long-period variable star, and an RR-Lyrae star, in order to
illustrate their use, applicability, and interpretation.
