  We apply the Hurst exponent idea for investigation of DJIA index time-series
data. The behavior of the local Hurst exponent prior to drastic changes in
financial series signal is analyzed. The optimal length of the time-window over
which this exponent can be calculated in order to make some meaningful
predictions is discussed. Our prediction hypothesis is verified with examples
of '29 and '87 crashes, as well as with more recent phenomena in stock market
from the period 1995-2003.Some interesting agreements are found.
