Abstract
In this chapter we analyze five international stock indices (Eurostoxx 50, Ibovespa, Nikkei 225, Sensex, and Standard & Poor’s 500, of Europe, Brazil, Japan, India, and USA, respectively) in order to check and measure their geometric complexity. From the financial point of view, we look for numerical differences in the wave patterns between emerging and consolidated economies. We are concerned with the discrimination of new and old markets, in a self-similar perspective. From the theoretical side, we wish to seek evidences pointing to a fractal structure of the daily closing prices. We wish to inquire about the type of randomness in the movement and evolution of the indices through different tests. Specifically, we use several procedures to find the suitability of an exponential law for the spectral power, in order to determine if the indices admit a model of colored noise and, in particular, a Brownian random pattern. Further, we check a possible structure of fractional Brownian motion as defined by Mandelbrot. For it, we determine several parameters from the spectral field and the fractal theory that quantify the values of the stock records and its trends.
The original version of this chapter was revised. An erratum to this chapter can be found at DOI 10.1007/978-3-319-28725-6_28
An erratum to this chapter can be found at http://dx.doi.org/10.1007/978-3-319-28725-6_28
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Navascués, M.A., Sebastián, M.V., Latorre, M. (2016). Stock Indices in Emerging and Consolidated Economies from a Fractal Perspective. In: Rojas, I., Pomares, H. (eds) Time Series Analysis and Forecasting. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-28725-6_9
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DOI: https://doi.org/10.1007/978-3-319-28725-6_9
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