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Anomalous volatility scaling in high frequency financial data

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  • Noemi Nava
  • T. Di Matteo
  • Tomaso Aste

Abstract

Volatility of intra-day stock market indices computed at various time horizons exhibits a scaling behaviour that differs from what would be expected from fractional Brownian motion (fBm). We investigate this anomalous scaling by using empirical mode decomposition (EMD), a method which separates time series into a set of cyclical components at different time-scales. By applying the EMD to fBm, we retrieve a scaling law that relates the variance of the components to a power law of the oscillating period. In contrast, when analysing 22 different stock market indices, we observe deviations from the fBm and Brownian motion scaling behaviour. We discuss and quantify these deviations, associating them to the characteristics of financial markets, with larger deviations corresponding to less developed markets.

Suggested Citation

  • Noemi Nava & T. Di Matteo & Tomaso Aste, 2015. "Anomalous volatility scaling in high frequency financial data," Papers 1503.08465, arXiv.org, revised Dec 2015.
  • Handle: RePEc:arx:papers:1503.08465
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    References listed on IDEAS

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    3. Muller, Ulrich A. & Dacorogna, Michel M. & Olsen, Richard B. & Pictet, Olivier V. & Schwarz, Matthias & Morgenegg, Claude, 1990. "Statistical study of foreign exchange rates, empirical evidence of a price change scaling law, and intraday analysis," Journal of Banking & Finance, Elsevier, vol. 14(6), pages 1189-1208, December.
    4. Guo, Zhenhai & Zhao, Weigang & Lu, Haiyan & Wang, Jianzhou, 2012. "Multi-step forecasting for wind speed using a modified EMD-based artificial neural network model," Renewable Energy, Elsevier, vol. 37(1), pages 241-249.
    5. M. Bartolozzi & C. Mellen & T. Di Matteo & T. Aste, 2007. "Multi-scale correlations in different futures markets," Papers 0707.3321, arXiv.org, revised Aug 2007.
    6. J. B. Glattfelder & A. Dupuis & R. B. Olsen, 2010. "Patterns in high-frequency FX data: discovery of 12 empirical scaling laws," Quantitative Finance, Taylor & Francis Journals, vol. 11(4), pages 599-614.
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    10. Barunik, Jozef & Aste, Tomaso & Di Matteo, T. & Liu, Ruipeng, 2012. "Understanding the source of multifractality in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(17), pages 4234-4251.
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    12. M. Bartolozzi & C. Mellen & T. Di Matteo & T. Aste, 2007. "Multi-scale correlations in different futures markets," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 58(2), pages 207-220, July.
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    Cited by:

    1. Anagnostidis, P. & Varsakelis, C. & Emmanouilides, C.J., 2016. "Has the 2008 financial crisis affected stock market efficiency? The case of Eurozone," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 116-128.

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