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.

中文翻译：

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IBOVESPA 资产的多分形去趋势波动分析

有效市场假说（EMH）可以被认为是支持现代经济金融理论的核心支柱。然而，在过去的几年中，由于与长记忆、分形维数和肥尾相关的经验证据，EMH 一直是强烈反对的，这些是形成与 EMH 相对的理论的关键因素，称为分形市场假设 (FMH)。本文的目的是基于多重分形去趋势波动分析 (MF-DFA) 测试 Ibovespa 指数的九个成分资产的 EMH 的弱形式。我们的研究结果表明，整体缩放行为接近不相关状态、较低程度的多重分形、高分形指数的优势以及作为多重分形来源的广泛概率密度函数。鉴于这种，