  The correlated Wishart model provides the standard benchmark when analyzing
time series of any kind. Unfortunately, the real case, which is the most
relevant one in applications, poses serious challenges for analytical
calculations. Often these challenges are due to square root singularities which
cannot be handled using common random matrix techniques. We present a new way
to tackle this issue. Using supersymmetry, we carry out an anlaytical study
which we support by numerical simulations. For large but finite matrix
dimensions, we show that statistical properties of the fully correlated real
Wishart model generically approach those of a correlated real Wishart model
with doubled matrix dimensions and doubly degenerate empirical eigenvalues.
This holds for the local and global spectral statistics. With Monte Carlo
simulations we show that this is even approximately true for small matrix
dimensions. We explicitly investigate the $k$-point correlation function as
well as the distribution of the largest eigenvalue for which we find a
surprisingly compact formula in the doubly degenerate case. Moreover we show
that on the local scale the $k$-point correlation function exhibits the sine
and the Airy kernel in the bulk and at the soft edges, respectively. We also
address the positions and the fluctuations of the possible outliers in the
data.
