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Fractal Properties in Economics

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  • H. Takayasu
  • M. Takayasu
  • M. P. Okazaki
  • K. Marumo
  • T. Shimizu

Abstract

Scaling properties in financial fluctuations are reviewed from the standpoint of statistical physics. We firstly show theoretically that the balance of demand and supply enhances fluctuations due to the underlying phase transition mechanism. By analyzing tick data of yen-dollar exchange rates we confirm two fractal properties: 1 The distribution of rate change in a fixed ticks is approximated by a symmetric stretched exponential function for a wide range of time intervals; 2 the interval time distribution of trades nearly follows a power law. Empirical fractal properties in companies' financial data, such as distributions and fluctuations in assets and incomes are discussed with a simple model. The importance of methods and theories for phase transitions is discussed.

Suggested Citation

  • H. Takayasu & M. Takayasu & M. P. Okazaki & K. Marumo & T. Shimizu, 2000. "Fractal Properties in Economics," Papers cond-mat/0008057, arXiv.org, revised Aug 2000.
    • Handle: RePEc:arx:papers:cond-mat/0008057
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    References listed on IDEAS

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    1. Sato, Aki-Hiro & Takayasu, Hideki, 1998. "Dynamic numerical models of stock market price: from microscopic determinism to macroscopic randomness," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 250(1), pages 231-252.
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    Cited by:

    1. Kim, Kyungsik & Yoon, Seong-Min, 2004. "Multifractal features of financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 272-278.
    2. Arthur Matsuo Yamashita Rios de Sousa & Hideki Takayasu & Misako Takayasu, 2017. "Detection of statistical asymmetries in non-stationary sign time series: Analysis of foreign exchange data," PLOS ONE, Public Library of Science, vol. 12(5), pages 1-18, May.
    3. Ohira, Toru & Sazuka, Naoya & Marumo, Kouhei & Shimizu, Tokiko & Takayasu, Misako & Takayasu, Hideki, 2002. "Predictability of currency market exchange," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 308(1), pages 368-374.
    4. Ohnishi, Takaaki & Mizuno, Takayuki & Aihara, Kazuyuki & Takayasu, Misako & Takayasu, Hideki, 2004. "Statistical properties of the moving average price in dollar–yen exchange rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 207-210.
    5. Aiba, Yukihiro & Hatano, Naomichi & Takayasu, Hideki & Marumo, Kouhei & Shimizu, Tokiko, 2002. "Triangular arbitrage as an interaction among foreign exchange rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 310(3), pages 467-479.
    6. 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.
    7. Norouzzadeh, P. & Rahmani, B., 2006. "A multifractal detrended fluctuation description of Iranian rial–US dollar exchange rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 328-336.
    8. T. Mizuno & T. Watanabe, 2010. "A statistical analysis of product prices in online markets," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 76(4), pages 501-505, August.
    9. Aiba, Yukihiro & Hatano, Naomichi & Takayasu, Hideki & Marumo, Kouhei & Shimizu, Tokiko, 2003. "Triangular arbitrage and negative auto-correlation of foreign exchange rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 253-257.

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