  In this paper, three approaches to calculate the self-similarity exponent of
a time series are compared in order to determine which one performs best to
identify the transition from random efficient market behavior (EM) to herding
behavior (HB) and hence, to find out the beginning of a market bubble. In
particular, classical Detrended Fluctuation Analysis (DFA), Generalized Hurst
Exponent (GHE) and GM2 (one of Geometric Method-based algorithms) were applied
for self-similarity exponent calculation purposes. Traditionally, researchers
have been focused on identifying the beginning of a crash. Instead of this, we
are pretty interested in identifying the beginning of the transition process
from EM to a market bubble onset, what we consider could be more interesting.
The relevance of self-similarity index in such a context lies on the fact that
it becomes a suitable indicator which allows to identify the raising of HB in
financial markets. Overall, we could state that the greater the self-similarity
exponent in financial series, the more likely the transition process to HB
could start. This fact is illustrated through actual S\&P500 stocks.
