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

TL;DR

This study compares three methods for calculating the Hurst exponent to predict the transition from efficient market behavior to herding behavior, aiming to identify the onset of market bubbles in S&P 500 stocks.

Contribution

It evaluates and compares DFA, GHE, and GM2 methods for early detection of market bubble formation through self-similarity analysis.

Findings

GHE and GM2 outperform DFA in predicting market transitions.

Higher self-similarity exponents correlate with increased likelihood of bubble onset.

The approach provides a potential early warning indicator for market bubbles.

Abstract

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.