Ft 1), 21 (8) called conditional correlations. It was demonstrated that these conditional correlations are also not constant. Two types of change were found. Firstly, the correlations have a statistically signicant time trend and grow in time. The average increase in correlation over 30 years is 0.36. Secondly, correlations in periods of high volatility (high variance) are higher. To obtain this result, the following model for the correlation coecient was identied: t = ri,us ri,us

0 + ri,us 1 Sus t , where ri,us is the correlation coecient between the unexpected (unpredicted) components in the asset returns for the ith country and the US, St is a dummy variable that takes the value 1 if the estimated conditional variance of the US market for time t is greater than its unconditional (mean) value and 0 otherwise. The estimated coecient r1 is positive for all countries. The average over all countries for r0 is equal to 0.430, while the average turbulence eect r1 is 0.117 . Finally, it was demonstrated that other informational variables can explain more changes in correlations than just the high volatility low volatility binning.

The average correlation coecient for 13 equity markets (Europe + US) increased from 0.37 in June 1981September 1987 to 0.5 in November 1987February 1994. The amount of signicant principal components selected by Kaisers rule decreases from 3 (in both periods before October 1987) to 2 (in the period after October 1987) for all markets and even from 3 to 1 for 12 European markets . Of course, in average values for such long periods it is impossible to distinguish the consequences of the October 1987 catastrophe and a trend of correlation coecients (that is, presumably, nonlinear).

Non-stationarity of the correlation matrix was demonstrated in a detailed study of the nancial empirical correlation matrix of the 30 companies which Deutsche Aktienindex (DAX) comprised during the period 19881999 . The time interval (time window) is set to 30 and continuously moved over the whole period. It was evidenced that the drawups and the drawdowns of the global index (DAX) are governed, respectively, by dynamics of a signicantly distinct nature. The drawdowns are dominated by one strongly collective eigenstate with a large eigenvalue. The opposite applies to drawups: the largest eigenvalue moves down which is compensated by a simultaneous elevation of lower eigenvalues. Distribution of correlation coecients for these data have a distinctive bell-like shape both for one time window (inside one correlation matrix) and for ensemble of such sliding windows in a long time period.