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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, the power spectrum is written as   $$S_{uu}(\nu) = <|\widetilde{u(\nu)}|> $$  \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.}