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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.%  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. \makefig{https://www.authorea.com/users/3982/articles/112661/master/file/figures/K2S82FOV/K2S82FOV.png}{The positions of the 56 SDSS quasars (red) overlaid on the K2 campaign 8 field of view (blue) and the Stripe 82 region (green). The combined long term variability information from SDSS and short term variability information from Kepler will allow us to more tightly constrain out models in the future. } 
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\makefig{https://www.authorea.com/users/3982/articles/112661/master/file/figures/MasterGreensFunc_Sample36CalibratedrBand/MasterGreensFunc_Sample36CalibratedrBand.png}{Distribution of Green’s function for sample 36 r-band at 1, 2, and 3 σσ. Distribution of timescales at which the Green’s functions are maximized are plotted on the top with corresponding values of the right. We can see that the maximum value of the Green’s function increases with longer timescales. The median Green’s function maximizing timescale is on the order of 100 days with an e-folding time of around 300 days.}  Another useful tool for analyzing the variable properties of a light-curve is it's power spectrum. This relates the variance between observations to the frequency at which they are observed. For SDSS data, estimating the true power-spectrum from the periodogram is difficult because of the irregularity and infrequency of the sampling. The CARMA model however allows us to make a theoretical prediction of what the power spectrum should look like fairly easily. For a CARMA(p,q) process, $u(t)$,  the power spectrum is written defined  as $$ S_{uu}(\nu) = \langle\mid\widetilde{u}(\nu)\mid^{2}\rangle $$    Where $\widetilde{u}(\nu)$ is the Fourier transform of $u(t)$. Since the power spectrum of a white noise process is a constant, $S_{dWdW} = \frac{1}{2\pi}$,  $$S_{uu}(\nu) = <|\widetilde{u(\nu)}|> $$  \makefig{https://www.authorea.com/users/3982/articles/112661/master/file/figures/PSD_Sample36CalibratedrBand/PSD_Sample36CalibratedrBand.png}{The relatively short sampling of this light-curve allows us to probe the power spectrum down to timescale as little as 3 days. Though the roots of the auto-regressive polynomial are complex, we don’t observe any strong PSD features as the widths of their Lorentzians are too large, smearing them out. Because of this, from inspection alone, it would be hard to distinguish this from an over-damped oscillator.}