Multifractal Detrended Fluctuations Analysis for Ibovespa Assets

The Efficient Market Hypothesis (EMH) can be considered the central pillar of support of the Modern Economic-Financial Theory. However, in the last few years, the EMH has been strongly contraried due to empirical evidence related to long-memory, fractal dimension and fat-tailed that were critical factors in formulating a theory opposed to EMH called Fractal Market Hypothesis (FMH). The purpose of this paper is to test the weak form of EMH for nine constituent assets of the Ibovespa index based on the Multifractal Detrended Fluctuations Analysis (MF-DFA). Our findings show overall scaling behavior approaching the uncorrelated regime, a lower degree of multifractality, the dominance of high fractal exponents, and a broad probability density function as the source of multifractality. Given this, Brazilian assets satisfied the EMH in the Fama’s sense because the multifractal properties inherent of time series returns for Brazilian assets tend to follow a random walk.