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Scaling, self-similarity and multifractality in FX markets

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  • Xu, Zhaoxia
  • Gençay, Ramazan

Abstract

This paper presents an empirical investigation of scaling and multifractal properties of US Dollar–Deutschemark (USD–DEM) returns. The data set is ten years of 5-min returns. The cumulative return distributions of positive and negative tails at different time intervals are linear in the double logarithmic space. This presents strong evidence that the USD–DEM returns exhibit power-law scaling in the tails. To test the multifractal properties of USD–DEM returns, the mean moment of the absolute returns as a function of time intervals is plotted for different powers of absolute returns. These moments show different slopes for these powers of absolute returns. The nonlinearity of the scaling exponent indicates that the returns are multifractal.

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Bibliographic Info

Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

Volume (Year): 323 (2003)
Issue (Month): C ()
Pages: 578-590

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Handle: RePEc:eee:phsmap:v:323:y:2003:i:c:p:578-590

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Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

Related research

Keywords: Scaling; Self-similarity; Multifractality; High-frequency data; Foreign exchange markets;

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Cited by:
  1. Cajueiro, Daniel O. & Tabak, Benjamin M., 2006. "Testing for predictability in equity returns for European transition markets," Economic Systems, Elsevier, vol. 30(1), pages 56-78, March.
  2. Sergio Da Silva, 2004. "Exponentially Damped Levy Flights, Multiscaling, and Exchange Rates," Finance 0405027, EconWPA.
  3. Hartmann, András & Mukli, Péter & Nagy, Zoltán & Kocsis, László & Hermán, Péter & Eke, András, 2013. "Real-time fractal signal processing in the time domain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(1), pages 89-102.
  4. Cajueiro, Daniel O. & Gogas, Periklis & Tabak, Benjamin M., 2009. "Does financial market liberalization increase the degree of market efficiency? The case of the Athens stock exchange," International Review of Financial Analysis, Elsevier, vol. 18(1-2), pages 50-57, March.
  5. Wang, Dong-Hua & Yu, Xiao-Wen & Suo, Yuan-Yuan, 2012. "Statistical properties of the yuan exchange rate index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(12), pages 3503-3512.
  6. Kang, Sang Hoon & Cheong, Chongcheul & Yoon, Seong-Min, 2013. "Intraday volatility spillovers between spot and futures indices: Evidence from the Korean stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(8), pages 1795-1802.
  7. Mauricio Labadie & Charles-Albert Lehalle, 2012. "Optimal starting times, stopping times and risk measures for algorithmic trading," Working Papers hal-00705056, HAL.
  8. Ahmet Sensoy & Benjamin M. Tabak, 2013. "How Much Random Does European Union Walk? A Time-Varying Long Memory Analysis," Working Paper 12, Research and Business Development Department, Borsa Istanbul.
  9. Suárez-García, Pablo & Gómez-Ullate, David, 2014. "Multifractality and long memory of a financial index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 226-234.
  10. Sergio Da Silva, 2004. "International Finance, Levy Distributions, and the Econophysics of Exchange Rates," International Finance 0405018, EconWPA.
  11. Batten, Jonathan A. & Kinateder, Harald & Wagner, Niklas, 2014. "Multifractality and value-at-risk forecasting of exchange rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 401(C), pages 71-81.
  12. Mauricio Labadie & Charles-Albert Lehalle, 2012. "Optimal starting times, stopping times and risk measures for algorithmic trading: Target Close and Implementation Shortfall," Papers 1205.3482, arXiv.org, revised Dec 2013.
  13. Jiang, Zhi-Qiang & Zhou, Wei-Xing, 2008. "Multifractality in stock indexes: Fact or Fiction?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(14), pages 3605-3614.
  14. Seemann, Lars & McCauley, Joseph L. & Gunaratne, Gemunu H., 2011. "Intraday volatility and scaling in high frequency foreign exchange markets," International Review of Financial Analysis, Elsevier, vol. 20(3), pages 121-126, June.

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