  This work develops application techniques for stochastic modelling of Active
Galactic Nuclei (AGN) variability as a probe of accretion disk physics.
Stochastic models, specifically Continuous Auto-Regressive Moving Average
(CARMA) models, characterize lightcurves by estimating delay timescales that
describe movements away from and toward equilibrium (mean flux) as well as an
amplitude and frequency of intrinsic perturbations to the AGN flux. We begin
this tutorial by reviewing discrete auto-regressive (AR) and moving-average
(MA) processes, we bridge these components to their continuous analogs, and
lastly we investigate the significance of timescales from direct stochastic
modelling of a lightcurve projected in power spectrum (PSD) and structure
function (SF) space. We determine that higher order CARMA models, for example
the Damped Harmonic Oscillator (DHO or CARMA(2,1)) are more sensitive to
deviations from a single-slope power-law description of AGN variability; unlike
Damped Random Walks (DRW or CAR(1)) where the PSD slope is fixed, the DHO slope
is not. Higher complexity stochastic models than the DRW capture additional
covariance in data and output additional characteristic timescales that probe
the driving mechanisms of variability.
