  We apply the concept of free random variables to doubly correlated (Gaussian)
Wishart random matrix models, appearing for example in a multivariate analysis
of financial time series, and displaying both inter-asset cross-covariances and
temporal auto-covariances. We give a comprehensive introduction to the rich
financial reality behind such models. We explain in an elementary way the main
techniques of the free random variables calculus, with a view to promote them
in the quantitative finance community. We apply our findings to tackle several
financially relevant problems, such as of an universe of assets displaying
exponentially decaying temporal covariances, or the exponentially weighted
moving average, both with an arbitrary structure of cross-covariances.
