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Relative fractional dynamics of stock markets

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Abstract

This paper analyses motion of stock markets (SM) in the perspective of fractional calculus and introduces the concept of relative fractional dynamics. The SM are characterized by long-range correlations and persistent memory. These features are found in natural and artificial systems and are well modelled by means of the tools of fractional calculus. The time series of daily closing prices of 11 SM for the period 9 July 1987 to 22 April 2016 are interpreted as motion trajectories and their distances analysed through the Fourier transform. The amplitude spectra are approximated by power law functions, characterizing the relative motion of the financial indices and their slow tendency to synchronize.

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Acknowledgments

The authors thank the Yahoo Finance (https://finance.yahoo.com/) for the dataset.

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Authors and Affiliations

  1. Department of Electrical Engineering, Institute of Engineering, Polytechnic of Porto, R. Dr. António Bernardino de Almeida, 431, 4249-015, Porto, Portugal

    J. A. Tenreiro Machado

  2. UISPA–LAETA/INEGI, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal

    António M. Lopes

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  1. J. A. Tenreiro Machado
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Correspondence to António M. Lopes.

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Tenreiro Machado, J.A., Lopes, A.M. Relative fractional dynamics of stock markets. Nonlinear Dyn 86, 1613–1619 (2016). https://doi.org/10.1007/s11071-016-2980-1

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