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Inverse Statistics in the Foreign Exchange Market

Author

Listed:
  • M. H. Jensen

    (Niels Bohr Institute, Denmark)

  • A. Johansen

    (My house, Humlebaek, Denmark)

  • F. Petroni

    (Dipartimento di Matematica and I.N.F.M. Universita dell'Aquila,, Italy)

  • I. Simonsen

    (Department of Physics, NTNU, Trondheim, Norway)

Abstract

We investigate intra-day foreign exchange (FX) time series using the inverse statistic analysis developed in [1,2]. Specifically, we study the time-averaged distributions of waiting times needed to obtain a certain increase (decrease) $\rho$ in the price of an investment. The analysis is performed for the Deutsch mark (DM) against the $US for the full year of 1998, but similar results are obtained for the Japanese Yen against the $US. With high statistical significance, the presence of "resonance peaks" in the waiting time distributions is established. Such peaks are a consequence of the trading habits of the markets participants as they are not present in the corresponding tick (business) waiting time distributions. Furthermore, a new {\em stylized fact}, is observed for the waiting time distribution in the form of a power law Pdf. This result is achieved by rescaling of the physical waiting time by the corresponding tick time thereby partially removing scale dependent features of the market activity.

Suggested Citation

  • M. H. Jensen & A. Johansen & F. Petroni & I. Simonsen, 2004. "Inverse Statistics in the Foreign Exchange Market," Papers cond-mat/0402591, arXiv.org, revised Mar 2004.
    • Handle: RePEc:arx:papers:cond-mat/0402591
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    Cited by:

    1. Guglielmo D'Amico & Filippo Petroni, 2012. "Weighted-indexed semi-Markov models for modeling financial returns," Papers 1205.2551, arXiv.org, revised Jun 2012.
    2. Restocchi, Valerio & McGroarty, Frank & Gerding, Enrico, 2019. "The stylized facts of prediction markets: Analysis of price changes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 159-170.
    3. Zhou, Wei-Xing & Yuan, Wei-Kang, 2005. "Inverse statistics in stock markets: Universality and idiosyncracy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 353(C), pages 433-444.
    4. G. D'Amico & F. Petroni & F. Prattico, 2013. "Semi-Markov Models in High Frequency Finance: A Review," Papers 1312.3894, arXiv.org.
    5. Michele Caraglio & Fulvio Baldovin & Attilio L. Stella, 2021. "How Fast Does the Clock of Finance Run?—A Time-Definition Enforcing Stationarity and Quantifying Overnight Duration," JRFM, MDPI, vol. 14(8), pages 1-15, August.
    6. Guglielmo D'Amico & Filippo Petroni, 2013. "Multivariate high-frequency financial data via semi-Markov processes," Papers 1305.0436, arXiv.org.
    7. Zou, Yongjie & Li, Honggang, 2014. "Time spans between price maxima and price minima in stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 303-309.

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