This article examines empirically the behavior of the correlation
between the return of shares listed on the BMF& BOVESPA over the period
from 2000 to 2015. To this end, we use multivariate GARCH models introduced
by Bollerslev (1990) to remove the temporal series of arrays of conditional
correlation of returns of stocks. With the temporal series of the largest
eigenvalues of matrices of correlation estimated conditional, we apply
statistical tests (unit root, structural breaks and trend) to verify the
existence of stochastic trend or deterministic to the intensity of the
correlation between the returns of the shares represented by eigenvalues.
Our results confirm that both in times of crises at national and
international turbulence, there is greater correlation between the actions.
However, we did not find any long-term trend in time series of the largest
eigenvalues of matrices of correlation conditional.