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The foreign exchange market: return distributions, multifractality, anomalous multifractality and Epps effect


  • Stanislaw Drozdz
  • Jaroslaw Kwapien
  • Pawel Oswiecimka
  • Rafal Rak


We present a systematic study of various statistical characteristics of high-frequency returns from the foreign exchange market. This study is based on six exchange rates forming two triangles: EUR-GBP-USD and GBP-CHF-JPY. It is shown that the exchange rate return fluctuations for all the pairs considered are well described by the nonextensive statistics in terms of q-Gaussians. There exist some small quantitative variations in the nonextensivity q-parameter values for different exchange rates and this can be related to the importance of a given exchange rate in the world's currency trade. Temporal correlations organize the series of returns such that they develop the multifractal characteristics for all the exchange rates with a varying degree of symmetry of the singularity spectrum f(alpha) however. The most symmetric spectrum is identified for the GBP/USD. We also form time series of triangular residual returns and find that the distributions of their fluctuations develop disproportionately heavier tails as compared to small fluctuations which excludes description in terms of q-Gaussians. The multifractal characteristics for these residual returns reveal such anomalous properties like negative singularity exponents and even negative singularity spectra. Such anomalous multifractal measures have so far been considered in the literature in connection with the diffusion limited aggregation and with turbulence. We find that market inefficiency on short time scales leads to the occurrence of the Epps effect on much longer time scales. Although the currency market is much more liquid than the stock markets and it has much larger transaction frequency, the building-up of correlations takes up to several hours - time that does not differ much from what is observed in the stock markets. This may suggest that non-synchronicity of transactions is not the unique source of the observed effect.

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  • Stanislaw Drozdz & Jaroslaw Kwapien & Pawel Oswiecimka & Rafal Rak, 2010. "The foreign exchange market: return distributions, multifractality, anomalous multifractality and Epps effect," Papers 1011.2385,
  • Handle: RePEc:arx:papers:1011.2385

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    References listed on IDEAS

    1. Adlai Fisher & Laurent Calvet & Benoit Mandelbrot, 1997. "Multifractality of Deutschemark/US Dollar Exchange Rates," Cowles Foundation Discussion Papers 1166, Cowles Foundation for Research in Economics, Yale University.
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    1. repec:eee:phsmap:v:494:y:2018:i:c:p:454-464 is not listed on IDEAS
    2. Chapeau-Blondeau, François, 2014. "Tsallis entropy for assessing quantum correlation with Bell-type inequalities in EPR experiment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 414(C), pages 204-215.
    3. Mali, Provash & Mukhopadhyay, Amitabha, 2014. "Multifractal characterization of gold market: A multifractal detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 413(C), pages 361-372.
    4. Aki-Hiro Sato & Takaki Hayashi & Janusz Hołyst, 2012. "Comprehensive analysis of market conditions in the foreign exchange market," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 7(2), pages 167-179, October.
    5. Robert Gk{e}barowski & Stanis{l}aw Dro.zd.z & Andrzej Z. G'orski & Pawe{l} O'swik{e}cimka, 2014. "Competition of Commodities for the Status of Money in an Agent-based Model," Papers 1412.2124,
    6. Provash Mali & Amitabha Mukhopadhyay, 2015. "Multifractal characterization of gold market: a multifractal detrended fluctuation analysis," Papers 1506.08847,

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