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Patterns in high-frequency FX data: Discovery of 12 empirical scaling laws

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  • J. B. Glattfelder
  • A. Dupuis
  • R. B. Olsen

Abstract

We have discovered 12 independent new empirical scaling laws in foreign exchange data-series that hold for close to three orders of magnitude and across 13 currency exchange rates. Our statistical analysis crucially depends on an event-based approach that measures the relationship between different types of events. The scaling laws give an accurate estimation of the length of the price-curve coastline, which turns out to be surprisingly long. The new laws substantially extend the catalogue of stylised facts and sharply constrain the space of possible theoretical explanations of the market mechanisms.

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  • J. B. Glattfelder & A. Dupuis & R. B. Olsen, 2008. "Patterns in high-frequency FX data: Discovery of 12 empirical scaling laws," Papers 0809.1040, arXiv.org, revised Jun 2010.
    • Handle: RePEc:arx:papers:0809.1040
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    1. J. Doyne Farmer & Fabrizio Lillo, 2003. "On the origin of power law tails in price fluctuations," Papers cond-mat/0309416, arXiv.org, revised Jan 2004.
    2. Sornette, Didier, 2001. "Fokker–Planck equation of distributions of financial returns and power laws," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 290(1), pages 211-217.
    3. Galluccio, S. & Caldarelli, G. & Marsili, M. & Zhang, Y.-C., 1997. "Scaling in currency exchange," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(3), pages 423-436.
    4. Ballocchi, Giuseppe & Dacorogna, Michel M. & Hopman, Carl M. & Muller, Ulrich A. & Olsen, Richard B., 1999. "The intraday multivariate structure of the Eurofutures markets," Journal of Empirical Finance, Elsevier, vol. 6(5), pages 479-513, December.
    5. Matteo, T. Di & Aste, T. & Dacorogna, Michel M., 2005. "Long-term memories of developed and emerging markets: Using the scaling analysis to characterize their stage of development," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 827-851, April.
    6. Geoffrey B. West & James H. Brown & Brian J. Enquist, 1997. "A General Model for the Origin of Allometric Scaling Laws in Biology," Working Papers 97-03-019, Santa Fe Institute.
    7. 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.
    8. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
    9. Xavier Gabaix & Parameswaran Gopikrishnan & Vasiliki Plerou & H. Eugene Stanley, 2003. "A theory of power-law distributions in financial market fluctuations," Nature, Nature, vol. 423(6937), pages 267-270, May.
    10. J-P. Bouchaud, 2001. "Power laws in economics and finance: some ideas from physics," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 105-112.
    11. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    12. Gençay, Ramazan & Dacorogna, Michel & Muller, Ulrich A. & Pictet, Olivier & Olsen, Richard, 2001. "An Introduction to High-Frequency Finance," Elsevier Monographs, Elsevier, edition 1, number 9780122796715.
    13. T. Di Matteo, 2007. "Multi-scaling in finance," Quantitative Finance, Taylor & Francis Journals, vol. 7(1), pages 21-36.
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    Cited by:

    1. T. Bisig & A. Dupuis & V. Impagliazzo & R. B. Olsen, 2012. "The scale of market quakes," Quantitative Finance, Taylor & Francis Journals, vol. 12(4), pages 501-508, July.
    2. Nava, Noemi & Di Matteo, T. & Aste, Tomaso, 2016. "Anomalous volatility scaling in high frequency financial data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 434-445.
    3. Denis M. Filatov & Maksim A. Vanyarkho, 2014. "An Unconventional Attempt to Tame Mandelbrot's Grey Swans," Papers 1406.5718, arXiv.org.
    4. Aloud, Monira & Tsang, Edward & Olsen, Richard & Dupuis, Alexandre, 2012. "A directional-change event approach for studying financial time series," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 6, pages 1-17.
    5. Noemi Nava & T. Di Matteo & Tomaso Aste, 2015. "Anomalous volatility scaling in high frequency financial data," Papers 1503.08465, arXiv.org, revised Dec 2015.
    6. Aloud, Monira & Tsang, Edward & Olsen, Richard & Dupuis, Alexandre, 2011. "A directional-change events approach for studying financial time series," Economics Discussion Papers 2011-28, Kiel Institute for the World Economy (IfW Kiel).
    7. Vladimir Petrov & Anton Golub & Richard Olsen, 2019. "Instantaneous Volatility Seasonality of High-Frequency Markets in Directional-Change Intrinsic Time," JRFM, MDPI, vol. 12(2), pages 1-31, April.
    8. Thomas Chopping, 2014. "Scaling laws: a viable alternative to value at risk?," Quantitative Finance, Taylor & Francis Journals, vol. 14(5), pages 889-911, May.
    9. Edward P. K. Tsang & Ran Tao & Antoaneta Serguieva & Shuai Ma, 2017. "Profiling high-frequency equity price movements in directional changes," Quantitative Finance, Taylor & Francis Journals, vol. 17(2), pages 217-225, February.
    10. Monira Essa Aloud, 2016. "Time Series Analysis Indicators under Directional Changes: The Case of Saudi Stock Market," International Journal of Economics and Financial Issues, Econjournals, vol. 6(1), pages 55-64.
    11. Monira Essa Aloud, 2016. "Profitability of Directional Change Based Trading Strategies: The Case of Saudi Stock Market," International Journal of Economics and Financial Issues, Econjournals, vol. 6(1), pages 87-95.
    12. Anton Golub & Gregor Chliamovitch & Alexandre Dupuis & Bastien Chopard, 2014. "Multi-scale Representation of High Frequency Market Liquidity," Papers 1402.2198, arXiv.org.
    13. James B. Glattfelder & Thomas Bisig & Richard B. Olsen, 2014. "R&D Strategy Document," Papers 1405.6027, arXiv.org.
    14. Gapeev, Pavel V. & Rodosthenous, Neofytos & Chinthalapati, V.L Raju, 2019. "On the Laplace transforms of the first hitting times for drawdowns and drawups of diffusion-type processes," LSE Research Online Documents on Economics 101272, London School of Economics and Political Science, LSE Library.

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