On the fractal self-organization of the financial time series

Vladimir Hilarov

Ioffe Institute, St. Petersburg, Russia

Cite: Hilarov V. On the fractal self-organization of the financial time series. J. Digit. Sci. 4(1), 71 – 77 (2022). https://doi.org/10.33847/2686-8296.4.1_6

Abstract. Time series of five financial indexes daily returns were analyzed by means of multifractal and recurrence quantification analysis (RQA) methods. It is shown that a financial crisis in 2008 year is accompanied with the increase in determinism and fractal self-organization. Such regularity is noted as analogous to other nonlinear systems behavior in catastrophic situations. At the same time, the global Hürst coefficient is minimal during the crises instead of maximum for physical systems.

Keywords: nonlinear dynamical systems, multifractals, recurrence quantification analysis, catastrophes.

  1. Hilarov, V.L., Korsukov, V.E., Butenko, P.N., Svetlov, V.N.: Wavelet transform as a method for studying the fractal properties of the surface of amorphous metals under mechanical load. Phys. Solid State, 46, 1868–1872 (2004)
  2. Butenko P.N., Gilyarov V.L., Korsukov V.E., Korsukova M.M., Obidov B.A.: The Effect of Isochronous Annealing on the Surface Characteristics of Ni50Ti50 Metal Glass Ribbons. Technical Physics, 65, 205–210, (2020).
  3. Gibowicz S.J., Lasocki S.: Seismicity induced by mining: Ten years later In: Dmowska R., Saltzman B. Advances in Geophysics. vol. 44. Elsevier, pp. 39-181, (2001).
  4. Kasimova V.A., Kopylova G.N., Lyubushin A.A.: Variations in the Parameters of Background Seismic Noise during the Preparation Stages of Strong Earthquakes in the Kamchatka Region. Izvestiya. Physics of the Solid Earth, 54, 269–283, (2018).
  5. Hilarov V.L.: Detection of the Deterministic Component in Acoustic Emission Signals from Mechanically Loaded Rock Samples. Phys. Solid State, 57, 2204-2211, (2015).
  6. Damaskinskaya E.E., Hilarov V.L, Panteleev I.A., Gafurova, D.R., Frolov, D.I.: Statistical Regularities of Formation of a Main Crack in a Structurally Inhomogeneous Material under Various Deformation Conditions. Physics of the solid state, 60, 1821-1826, (2018). ‏
  7. Ivanov P. Ch., Amaral N L. A., Goldberger A. L., Havlin S., Rosenblum M. G., Struzikk Z R., Stanley H. E.: Multifractality in human heartbeat dynamics .Nature, 399,  461-465, (1999)
  8. Hilarov V.L.:Epileptic seizures regularities, revealed from encephalograms time series by nonlinear mechanics methods. J. Phys.: Conf. Ser., 1400 033011, 2019).
  9. Jiang Z.-Q., Xie W.-J., Zhou W.-X., Sornette D.: Multifractal analysis of financial markets: a review. Rep. Progr. Phys., 82, 125901, (2019).
  10. Jaffard S., Melot C., Leonarduzzi R., Wendt H., Abry P., Roux S.G., Torres M.E:. P-exponent and p-leaders, Part I: Negative pointwise regularity. Physica A448, 300-318, (2016).
  11. Leonarduzzi R., Wendt H., Abry P., Jaffard S., Melot C., Roux S.G., Torres M.E.: P-exponent and p-leaders, Part II: Multifractal analysis. Relations to detrended fluctuation analysis. Physica,  A448, 319-339, (2016).
  12. Wendt H., Roux S.G., Jaffard S., Abry P.: Wavelet leaders and bootstrap for multifractal analysis of images. Signal Process. 89, 1100-1114, (2009).
  13. Marwan N., Romano M.C., Thiel M., Kurths J. (2007). Recurrence plots for the analysis of complex systems. //Phys. Reports. V. 438. P. 237–329.
  14. https://finance.yahoo.com/world-indices/

Published online 12.06.2022