Modeling time variability of AGN with the CARMA models

AGN emission is variable in all energy bands, from radio to X/gamma-rays. There is evidence that this variability is stochastic in nature. I will present a class of continuous-time autoregressive moving average models (CARMA; Kelly et al. 2014) as a tool to characterize the variability features of AGN light curves across the electromagnetic spectrum. The power spectral density (PSD) of a CARMA model can be expressed as a sum of Lorentzian functions, which makes the method extremely flexible and able to model a broad range of PSDs. The CARMA code is designed to deal with non-uniformly sampled, gappy data sets, and thus it is a perfect tool to quantify the time variability of astronomical time series. It has statistically rigorous foundation as it provides the likelihood function for light curves sampled from CARMA processes and relies on a Bayesian method to infer the probability distribution of the PSD given the measured light curve. In particular, CARMA modeling allows us to infer the PSD frequencies of spectral breaks and/or quasi periodic oscillations, if present. These PSD features are importants imprints of the physical processes generating the variability and/or the physical properties of the regions emitting the variable radiation, such as the region's size and location. I will discuss our most recent results on the time variability of the gamma-ray lightcurves of Fermi/LAT blazars and multiband light curves of the BL Lac object, OJ 287, obtained by utilizing the CARMA models.