In the first part of this paper we present experimental evidence that the Mexican stock market has a fractal structure. We obtained the experimental results by using the Matsushita-Ouchi method, the box-counting method, and the fractal image compression technique of M. Barnsley. The results obtained by applying the Matsushita-Ouchi technique to the returns of the Indice de Precios y Cotizaciones (IPC) of the Mexican stock market support the assertion that the returns of the IPC behave like a fractional brownian motion. The box-counting method allows us to calculate the dimension of the graphs of the IPC, and its Hurst exponent H. The application of the fractal image compression technique produces attractors which are closed to the graphs of the returns of the IPC, and has permited us to estimate H. In the second part of the paper, we present two applications: first we study the efficiency graphs of the Mexican stock market, by plotting the Hurst exponent H as a funtion of time, and then we localize its structural changes by making use of a fractal attractor located in the phase space: H-IPC. We show that the fall of the IPC, that occurred between 1994 and 1995, corresponded to a rise of the value of H. We localize approximately the structural changes of the Mexican economy between 1987 and 1996.
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- The Fractal Structure, Efficiency, and Structural Change: The Case of the Mexican Stock Market
Carlos Alberto García-Valdéz
- Springer Berlin Heidelberg
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