  Financial markets are highly correlated systems that reveal both the
inter-market dependencies and the correlations among their different
components. Standard analyzing techniques include correlation coefficients for
pairs of signals and correlation matrices for rich multivariate data. In the
latter case one constructs a real symmetric matrix with real non-negative
eigenvalues describing the correlation structure of the data. However, if one
performs a correlation-function-like analysis of multivariate data, when a
stress is put on investigation of delayed dependencies among different types of
signals, one can calculate an asymmetric correlation matrix with complex
eigenspectrum. From the Random Matrix Theory point of view this kind of
matrices is closely related to Ginibre Orthogonal Ensemble (GinOE). We present
an example of practical application of such matrices in correlation analyses of
empirical data. By introducing the time lag, we are able to identify temporal
structure of the inter-market correlations. Our results show that the American
and German stock markets evolve almost simultaneously without a significant
time lag so that it is hard to find imprints of information transfer between
these markets. There is only an extremely subtle indication that the German
market advances the American one by a few seconds.
