Accelerating CARMA modeling with Gaussian Processes

Continuous-time autoregressive moving average (CARMA) processes have became increasingly popular in recent years owing to their success at modeling irregularly-spaced, time-series data and our growing capability of collecting/storing time-domain information. CARMA modeling has been employed in many scientific disciplines; in astronomy, its application is often found in AGN variability analysis. In fact, the extensively studied Damped Random Walk (DRW) model is the lowest order CARMA model—CARMA(1,0). However, the application of higher-order CARMA models to large data sets has been very limited mostly because of the high computational cost. Here, we introduce a new tool that can significantly speed up the process of fitting CARMA models to time series by utilizing ‘celerite', a fast gaussian process (GP) modeling library that can compute the likelihood for a certain class of GPs in O(NJ²) operations (where J is the number of components in the 'celerite’ GP kernel). We believe that the elevated performance will not only enable the application of CARMA modeling to much larger datasets, like those that will be generated by LSST, but will also help with exploring the intrinsic properties of CARMA processes through experiments that could not have been conducted without the help of supercomputers in the past.