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\section{Data}  Our sample consists of 56 spectroscopically confirmed quasar light curves from the seventh data release of the Sloan Digital Sky Survey (Schneider et al. 2010). These quasars range in redshift from $z = 0.19$ to $z = 3.83$ and in luminosity from $L = 10^{15} L_{\odot}$ to $L = 10^{20} L_{\odot}$. %  These samples were taken from the Southern Equitorial Stripe known as Stripe 82. Stripe 82 is a $275^{2}$ degree area of sky with repeated sampling centered on the celestial equator. It reaches 2 magnitudes deeper than SDSS single pass data going as deep as magnitude 23.5 in the r-band for galaxies with median seeing of 1.1'' (Annis et al. 2014).%  These samples were chosen because they exist in the field of the Kepler K2 mission's campaign 8. This will eventually give us a much denser data set with shorter cadence allowing us to probe far deeper into the short-term variability properties of these objects than would be possible with SDSS alone.% alone. %Talk more about Kepler  Each light curve contains photometric information from two bands (g and r) with as much as 10 years of data. The number of epochs of data range from 29 observations to 81 observations in all photometric bands with sampling intervals ranging from one day to two years. This inconsistent sampling will lead to issues with our analysis which will be discussed later. %  PSF magnitudes are calibrated using a set of standard stars (Ivezic et al 2007) to reduce the error in our data down to 1\%. We then convert these magnitudes to fluxes for our analysis and convert observed time sampling intervals to the rest frame of the quasar. %  We use asinh magnitudes (also referred to as "Luptitudes") for flux conversion (York et al. 2000) (Lupton, Gunn, \& Szalay 1999) as is standard for SDSS.  
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\subsection{ARMA}  **Talk about using white noise to drive the process  There exist a class of finite difference equations used in the analysis of discrete time series known as autoregressive-moving average (ARMA) processes. These equations relate the autoregressive and moving average properties of a times series. (obvious) A stationary process $X_t$ is an ARMA(p,q) process if at every time $t$  $$X_t - \phi_1X_{t-1} - ... - \phi_pX_{t-p} = Z_t + \theta_{t-1} + ... + \theta_qZ_{t-q} $$  where ${Z_t}$ is a white noise process with zero mean and variance $\sigma^2$.  \!\!BE SURE TO CITE BROCKWELL AND DEVID TIME SERIES THEORY AND METHODS  **Quick intro to ARMA (an maybe a bit of stochastic analysis)  ***Background, current use  **White noise process -> "forcing term" -> ARMA  **Stationary process (requirement for ARMA and CARMA), define it  ** present equation  ** short hand with AR and MA polynomials (do this for CARMA too to make it easier to work with polynomials)  **Autogressive behavior  ***AR(1) process  **Moving average behavior (show why stationary)  **ARMA is discrete, mention why we need a continuous method instead  \subsection{CARMA}  A continuous-time ARMA (CARMA) process is the continuous case of the discrete ARMA process. A system described by a CARMA process obeys the stochastic differential equation