  Correlations between random variables play an important role in applications,
e.g.\ in financial analysis. More precisely, accurate estimates of the
correlation between financial returns are crucial in portfolio management. In
particular, in periods of financial crisis, extreme movements in asset prices
are found to be more highly correlated than small movements. It is precisely
under these conditions that investors are extremely concerned about changes on
correlations. A binary segmentation procedure to detect the number and position
of multiple change points in the correlation structure of random variables is
proposed. The procedure assumes that expectations and variances are constant
and that there are sudden shifts in the correlations. It is shown analytically
that the proposed algorithm asymptotically gives the correct number of change
points and the change points are consistently estimated. It is also shown by
simulation studies and by an empirical application that the algorithm yields
reasonable results.
