Abstract
The Efficient Market Hypothesis (EMH) has been repeatedly demonstrated to be an inferior — or at best incomplete — model of financial market behavior. The Fractal Market Hypothesis (FMH) has been installed as a viable alternative to the EMH. The FMH asserts that markets are stabilized by matching demand and supply of investors’ investment horizons while the EMH assumes that the market is at equilibrium. A quantity known as the Hurst exponent determines whether a fractal time series evolves by random walk, a persistent trend or mean reverts. The time dependence of this quantity is explored for two developed market indices and one emerging market index. Another quantity, the fractal dimension of a time series, provides an indicator for the onset of chaos when market participants behave in the same way and breach a given threshold. A relationship is found between these quantities: the larger the change in the fractal dimension before breaching, the larger the rally in the price index after the breach. In addition, breaches are found to occur principally during times when the market is trending.
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