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Fractal Analysis of Financial Time Series Using Fractal Dimension and Pointwise Hölder Exponents

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  • Agnieszka Kapecka

    () (Warsaw School of Economics)

Abstract

This paper presents a fractal analysis application to the verification of assumptions of Fractal Market Hypothesis and the presence of fractal properties in financial time series. In this research, the box-counting dimension and pointwise Hölder exponents are used. Achieved results lead to interesting observations related to nonrandomness of price series and occurrence of relationships binding fractal properties and variability measures with the presence of trends and influence of the economic situation on financial instruments’ prices.

Suggested Citation

  • Agnieszka Kapecka, 2013. "Fractal Analysis of Financial Time Series Using Fractal Dimension and Pointwise Hölder Exponents," Dynamic Econometric Models, Uniwersytet Mikolaja Kopernika, vol. 13, pages 107-126.
  • Handle: RePEc:cpn:umkdem:v:13:y:2013:p:107-126
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    References listed on IDEAS

    as
    1. Sánchez Granero, M.A. & Trinidad Segovia, J.E. & García Pérez, J., 2008. "Some comments on Hurst exponent and the long memory processes on capital markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(22), pages 5543-5551.
    2. Cajueiro, Daniel O & Tabak, Benjamin M, 2004. "The Hurst exponent over time: testing the assertion that emerging markets are becoming more efficient," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(3), pages 521-537.
    3. Alvarez-Ramirez, Jose & Alvarez, Jesus & Rodriguez, Eduardo & Fernandez-Anaya, Guillermo, 2008. "Time-varying Hurst exponent for US stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(24), pages 6159-6169.
    4. B. Mandelbrot, 1972. "Statistical Methodology for Nonperiodic Cycles: From the Covariance To R/S Analysis," NBER Chapters,in: Annals of Economic and Social Measurement, Volume 1, number 3, pages 259-290 National Bureau of Economic Research, Inc.
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    More about this item

    Keywords

    fractal analysis; fractal dimension; box-counting dimension; pointwise Hölder exponents; Hurst exponent.;

    JEL classification:

    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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