  AGN exhibit rapid, high amplitude stochastic flux variations across the
entire electromagnetic spectrum on timescales ranging from hours to years. The
cause of this variability is poorly understood. We present a Green's
Function-based method for using variability to (1) measure the time-scales on
which flux perturbations evolve and (2) characterize the driving flux
perturbations. We model the observed light curve of an AGN as a linear
differential equation driven by stochastic impulses. We analyze the light curve
of the Kepler AGN Zw 229-15 and find that the observed variability behavior can
be modeled as a damped harmonic oscillator perturbed by a colored noise
process. The model powerspectrum turns over on time-scale $385$~d. On shorter
time-scales, the log-powerspectrum slope varies between $2$ and $4$, explaining
the behavior noted by previous studies. We recover and identify both the
$5.6$~d and $67$~d timescales reported by previous work using the Green's
Function of the C-ARMA equation rather than by directly fitting the
powerspectrum of the light curve. These are the timescales on which flux
perturbations grow, and on which flux perturbations decay back to the
steady-state flux level respectively. We make the software package KALI used to
study light curves using our method available to the community.
