Asymmetry Effect in Fractal Organization of Financial Time Series

Paweł Oświęcimka 1Stanisław Drożdż 1,2

1. Polish Academy of Sciences, Institute of Nuclear Physics (IFJ PAN), Radzikowskiego 152, Kraków 31-342, Poland
2. Cracow University of Technology, Institute of Computing Science, Al. Jana Pawła II 37, Kraków 31-864, Poland

Abstract

In recent years, many natural systems are identified to demonstrate multiscale organization, which can be quantitatively described within the framework of the multifractal formalism and the related singularity spectra. The mathematical cascade-like models are characterized by a singularity spectrum whose shape is typically similar to an inverted symmetric parabola, whereas for empirical data we usually obtain asymmetrical spectra. This presentation shows that asymmetry in the singularity spectrum provides important information about nonuniform organization of the fractal time series. We show that financial time series are characterized mainly by the left-sided spectrum asymmetry that can be interpreted as an indication of the multifractal organization of large events, while the dynamics of small  ones is less complex and can be regarded as a kind of noise. On the other hand, the right-sided spectrum asymmetry occurs less frequently and is less intuitive. It has been identified, for example, in the intertransaction intervals. This shape suggests the multifractal organization of small fluctuations and monofractality of the large ones. We also present models that are able to generate the signals with a given type of asymmetry in their singularity spectra, which support our interpretation of the asymmetry phenomenon.

 

Related papers
  1. Volatility correlations in narrative
  2. Multifractal cross-correlation and casual direction between energy and financial markets in 2014-2016
  3. Correlation structure decomposition through scale- and amplitude-dependent qMST methodology  
  4. Technological stock market revolution from multifractal perspective
  5. Zipf distribution related characteristics of punctuation marks in narrative texts
  6. Complexity characteristics of world econo- and sociophysics scientific collaboration network
  7. The generalized detrended cross-correlation coefficient ρq and its application to financial data.
  8. Agent-based modelling of commodity market dynamics
  9. Literary and scientific texts in network representation
  10. Complexity: what it is and how it can be identified
  11. Hurst exponent as a tool of technical analysis in the foreign exchange market
  12. Effect of detrending on multifractal characteristics
  13. Current world markets development from log-periodic perspective
  14. Accuracy of the box-counting algorithm for noisy fractals
  15. World markets development from log-periodic perspective
  16. Long-range dependences in natural language
  17. Accuracy analysis of the box counting algorithm
  18. Characteristics of distributions for the stock returns and trading volumes
  19. Financial extreme events with negative fractal dimensions.
  20.   Statistical and network-based analysis of English and Polish literary texts.
  21. Foreign currency network: its structure, evolution and subtle interactions
  22. Fractals, log-periodicity and financial crashes
  23. Modelling emergence of money
  24. Time correlations in currency exchange rates
  25. Analysis of a network structure of the foreign currency exchange market
  26. Internal organization of languages: Decomposing "Ulysses"
  27. Asymmetric fractal properties of positive and negative returns
  28. Current status of financial log-periodicity
  29. Cross-correlations in Warsaw Stock Exchange
  30. Power like scaling in Minimal Spanning Tree Graphs for FOREX networks
  31. Non-Hermitean matrices in an analysis of financial correlations
  32. Multifractal Model of Asset Returns versus real stock market dynamics
  33. Complexity characteristics of currency networks
  34. Correlation matrix decomposition of intraday WIG20 fluctuations
  35. Statistical properties of stock market eigensignals
  36. A comparative study of the applicability of the MF-DFA and the wavelet methods in the context of financial data
  37. Measuring subtle effects of persistence in the stock market dynamics

Presentation: Invited oral at 8 Ogólnopolskie Sympozjum "Fizyka w Ekonomii i Naukach Społecznych", by Paweł Oświęcimka
See On-line Journal of 8 Ogólnopolskie Sympozjum "Fizyka w Ekonomii i Naukach Społecznych"

Submitted: 2015-08-28 23:44
Revised:   2015-08-28 23:44