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A mathematical definition of the financial bubbles and crashes

Author

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  • Watanabe, Kota
  • Takayasu, Hideki
  • Takayasu, Misako

Abstract

We check the validity of the mathematical method of detecting financial bubbles or crashes, which is based on a data fitting with an exponential function. We show that the period of a bubble can be determined nearly uniquely independent of the precision of data. The method is widely applicable for stock market data such as the Internet bubble.

Suggested Citation

  • Watanabe, Kota & Takayasu, Hideki & Takayasu, Misako, 2007. "A mathematical definition of the financial bubbles and crashes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(1), pages 120-124.
    • Handle: RePEc:eee:phsmap:v:383:y:2007:i:1:p:120-124
    DOI: 10.1016/j.physa.2007.04.093
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    Citations

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    Cited by:

    1. Nora CHIRIȚĂ & Camelia DELCEA & Ionuț NICA & Simona-Liliana CRĂCIUNESCU (PARAMON) & Ștefan-Andrei IONESCU, 2023. "Financial contagion and identifying speculative frenzies: Unraveling price bubbles in cryptocurrency markets," Theoretical and Applied Economics, Asociatia Generala a Economistilor din Romania / Editura Economica, vol. 0(3(636), A), pages 21-40, Autumn.
    2. Zhang, Qunzhi & Sornette, Didier & Balcilar, Mehmet & Gupta, Rangan & Ozdemir, Zeynel Abidin & Yetkiner, Hakan, 2016. "LPPLS bubble indicators over two centuries of the S&P 500 index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 458(C), pages 126-139.
    3. Ajmi, Ahdi Noomen & Hammoudeh, Shawkat & Mokni, Khaled, 2021. "Detection of bubbles in WTI, brent, and Dubai oil prices: A novel double recursive algorithm," Resources Policy, Elsevier, vol. 70(C).
    4. Hui, Eddie C.M. & Zheng, Xian & Wang, Hui, 2010. "A dynamic mathematical test of international property securities bubbles and crashes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(7), pages 1445-1454.
    5. Marcelo M. de Oliveira & Alexandre C. L. Almeida, 2014. "Testing for rational speculative bubbles in the Brazilian residential real-estate market," Papers 1401.7615, arXiv.org.
    6. Huang, Weihong & Zheng, Huanhuan & Chia, Wai-Mun, 2010. "Financial crises and interacting heterogeneous agents," Journal of Economic Dynamics and Control, Elsevier, vol. 34(6), pages 1105-1122, June.
    7. Balcilar, Mehmet & Ozdemir, Zeynel Abidin & Yetkiner, Hakan, 2014. "Are there really bubbles in oil prices?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 631-638.
    8. Hervé OTT, 2012. "Fertilizer markets and its interplay with commodity and food prices," JRC Research Reports JRC73043, Joint Research Centre.
    9. Stéphane Goutte & David Guerreiro & Bilel Sanhaji & Sophie Saglio & Julien Chevallier, 2019. "International Financial Markets," Post-Print halshs-02183053, HAL.

    More about this item

    Keywords

    Financial market; Bubble; Crash;
    All these keywords.

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