A Tutorial on Fitting Time-Series With CARMA Models

A few prerequesites: you will need some code and libraries in order to follow along.

• Julia: an innovative Matlab-like language with C-like speeds, developed at MIT.
• Ensemble: a set of Julia libraries for sampling from probability distributions, loosely organised around the "affine invariant" algorithm underlying emcee and described by Goodman and Weare. Ensemble is not yet a part of the standard Julia package set, so you will have to install it directly from GitHub: Pkg.clone("https://github.com/farr/Ensemble.jl.git").
• CARMA: a set of Julia libraries for fitting CARMA models. See Kelly et al. (2014) for the methods.
• The Julia packages PyPlot and PyCall and the Python package seaborn to plot the results of your fits.
• IJulia: to allow the use of Juypter (formerly iPython) notebooks with Julia. Pkg.add("IJulia").

More Information

For more information on CARMA models, read Kelly, et al (2014) or the forthcoming Barrett & Farr (in prep). There is a similar package, carma_pack, associated with Kelly, et al (2014), but we have found it to be sometimes buggy.