Data

Our sample consists of 56 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). 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.

These samples also exist within the field of the Kepler K2 mission’s campaign 8. The Kepler space telescope’s original purpose was planet finding, which required that it quickly and consistently take many exposures over long periods of time in order to look for small periodic dips in the light from potential planetary systems. After the failure of two of the four reaction wheels, the telescope was limited in its pointing to its orbital plane, which is approximately the ecliptic. Due to limited mobility, the K2 project was started which involved having the telescope observe single regions of the sky for approximately 75 days at a time with observations every 30 minutes. (Howell et al. 2014). Fortuitously, one of these regions happens to overlap with Stripe 82, which means short term time-series data will soon be available for these objects. This increase in time sampling rate will allow us to probe far deeper into the short-term variability properties of these objects as compared to SDSS.

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Continuous-Time Auto Regressive Moving Average

ARMA

Analysis of astronomical time-dependent data sets requires methods of quantifying and parameterizing the properties of the observed process in order to learn about the underlying physical processes driving them. The most common method of parameterization of light curve variability currently is to compute the structure function. The structure function is useful because it allows us to relate the variation in brightness to the period of time over which we observe the change. The structure function can be characterized in a number of ways, the simplest of which is with a power law with a slope and y-intercept as free parameters [GTR: Add citation, e.g. Schmidt et al. 2010]. While a useful tool, the structure function lacks the sophistication required to probe the complex behavior of AGN. Instead, we l