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In this paper, three approaches to calculate the self-similarity exponent ofa time series are compared in order to determine which one performs best toidentify the transition from random efficient market behavior (EM) to herdingbehavior (HB) and hence, to find out the beginning of a market bubble. Inparticular, classical Detrended Fluctuation Analysis (DFA), Generalized HurstExponent (GHE) and GM2 (one of Geometric Method-based algorithms) were appliedfor self-similarity exponent calculation purposes. Traditionally, researchershave been focused on identifying the beginning of a crash. Instead of this, weare pretty interested in identifying the beginning of the transition processfrom 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 thatit becomes a suitable indicator which allows to identify the raising of HB infinancial markets. Overall, we could state that the greater the self-similarityexponent in financial series, the more likely the transition process to HBcould start. This fact is illustrated through actual S\&P500 stocks.

A comparison among some Hurst exponent approaches to predict nascent bubbles in $500$ company stocks