  There are many research papers yielding the financial data models, where
returns are tied either to the fundamental analysis or to the individual, often
irrational, behaviour of investors. In the second case the bubble followed by
the crisis is possible on the market. Such bubble or crisis is reflected by the
cross-correlated extreme positive or negative returns of many assets. Such
returns are modelled by the copula with the meaningful tail dependencies. The
typical model of such cross-correlation provides the t-Student copula. The
author demonstrates that the mutual information tied to this copula can be
measured by the 4th order multivariate cumulants. Tested on the artificial
data, the 4th order multivariate cumulant approach was used successfully for
the financial crisis detection. For this end the author introduces the outliers
detection algorithm. In addition this algorithm displays the potential
application for the crisis prediction, where the cross-correlated extreme
events may appear before the crisis in the analogy to the auto-correlated ones
measured by the Hurst Exponent.
