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Can log-periodic power law structures arise from random fluctuations?

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  • Wosnitza, Jan Henrik
  • Leker, Jens

Abstract

Recent research has established log-periodic power law (LPPL) patterns prior to the detonation of the German stock index (DAX) bubble in 1998. The purpose of this article is to explore whether a Langevin equation extracted from real world data can generate synthetic time series with comparable LPPL structures. To this end, we first estimate the stochastic process underlying the DAX log-returns during the period from mid-1997 until end-2003. The employed data set contains about 3.93⋅106 intraday DAX quotes at a sampling rate of 15 s. Our results indicate that the DAX log-returns can be described as a Markov process. As a consequence, a Langevin equation is derived. Based on this model equation, we run extensive simulations in order to generate 100 synthetic DAX trajectories each covering 3000 trading days. We find LPPL behavior in ten artificial time series. Moreover, we can establish a link between LPPL patterns and ensuing bubble bursts in seven synthetic 600-week windows. However, the LPPL components in most synthetic trajectories differ fundamentally from those LPPL structures that have previously been detected in real financial time series. Summarized, this paper demonstrates that LPPL structures are not necessarily the signature of imitative behavior among investors but can also stem from noise, even though the likelihood of this is extremely low. Thus, our findings confirm with high statistical confidence that the LPPL structures in the DAX development are rooted deeper than only in the random fluctuations of the German stock market.

Suggested Citation

  • Wosnitza, Jan Henrik & Leker, Jens, 2014. "Can log-periodic power law structures arise from random fluctuations?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 401(C), pages 228-250.
  • Handle: RePEc:eee:phsmap:v:401:y:2014:i:c:p:228-250
    DOI: 10.1016/j.physa.2014.01.007
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    References listed on IDEAS

    as
    1. Zhou, Wei-Xing & Sornette, Didier, 2006. "Fundamental factors versus herding in the 2000–2005 US stock market and prediction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 360(2), pages 459-482.
    2. Yan, Wanfeng & Woodard, Ryan & Sornette, Didier, 2012. "Leverage bubble," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 180-186.
      • Wanfeng Yan & Ryan Woodard & Didier Sornette, 2010. "Leverage Bubble," Papers 1011.0458, arXiv.org, revised Nov 2010.
    3. Clark, Andrew, 2004. "Evidence of log-periodicity in corporate bond spreads," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 338(3), pages 585-595.
    4. D. Sornette & A. Johansen, 2001. "Significance of log-periodic precursors to financial crashes," Papers cond-mat/0106520, arXiv.org.
    5. Sornette, Didier & Zhou, Wei-Xing, 2006. "Predictability of large future changes in major financial indices," International Journal of Forecasting, Elsevier, vol. 22(1), pages 153-168.
    6. A. P. Nawroth & J. Peinke, 2006. "Small scale behavior of financial data," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 50(1), pages 147-151, March.
    7. Didier Sornette & Wei-Xing Zhou, 2002. "The US 2000-2002 market descent: How much longer and deeper?," Quantitative Finance, Taylor & Francis Journals, vol. 2(6), pages 468-481.
    8. Jiang, Zhi-Qiang & Zhou, Wei-Xing & Sornette, Didier & Woodard, Ryan & Bastiaensen, Ken & Cauwels, Peter, 2010. "Bubble diagnosis and prediction of the 2005-2007 and 2008-2009 Chinese stock market bubbles," Journal of Economic Behavior & Organization, Elsevier, vol. 74(3), pages 149-162, June.
    9. D. Sornette, 2003. "Critical Market Crashes," Papers cond-mat/0301543, arXiv.org.
    10. Matsushita, Raul & da Silva, Sergio & Figueiredo, Annibal & Gleria, Iram, 2006. "Log-periodic crashes revisited," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 364(C), pages 331-335.
    11. N/A, 2000. "The High Exchange Rate," National Institute Economic Review, National Institute of Economic and Social Research, vol. 173(1), pages 9-11, July.
    12. George Chang & James Feigenbaum, 2006. "A Bayesian analysis of log-periodic precursors to financial crashes," Quantitative Finance, Taylor & Francis Journals, vol. 6(1), pages 15-36.
    13. D. Sornette & A. Johansen, 2001. "Significance of log-periodic precursors to financial crashes," Quantitative Finance, Taylor & Francis Journals, vol. 1(4), pages 452-471.
    14. Sornette, Didier & Johansen, Anders, 1997. "Large financial crashes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(3), pages 411-422.
    15. Nawroth, Andreas P. & Peinke, Joachim, 2007. "Medium and small-scale analysis of financial data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 193-198.
    16. Zhou, Wei-Xing & Sornette, Didier, 2008. "Analysis of the real estate market in Las Vegas: Bubble, seasonal patterns, and prediction of the CSW indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(1), pages 243-260.
    17. J.A. Feigenbaum, 2001. "A statistical analysis of log-periodic precursors to financial crashes-super-," Quantitative Finance, Taylor & Francis Journals, vol. 1(3), pages 346-360, March.
    18. Czarnecki, Łukasz & Grech, Dariusz & Pamuła, Grzegorz, 2008. "Comparison study of global and local approaches describing critical phenomena on the Polish stock exchange market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(27), pages 6801-6811.
    19. Anders Johansen & Didier Sornette, 2010. "Shocks, Crashes and Bubbles in Financial Markets," Brussels Economic Review, ULB -- Universite Libre de Bruxelles, vol. 53(2), pages 201-253.
    20. Yan, Wanfeng & Woodard, Ryan & Sornette, Didier, 2012. "Diagnosis and prediction of rebounds in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1361-1380.
    21. Renner, Ch. & Peinke, J. & Friedrich, R., 2001. "Evidence of Markov properties of high frequency exchange rate data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 298(3), pages 499-520.
    22. Wanfeng Yan & Ryan Woodard & Didier Sornette, 2010. "Diagnosis and Prediction of Tipping Points in Financial Markets: Crashes and Rebounds," Papers 1001.0265, arXiv.org, revised Feb 2010.
    23. W. -X. Zhou & D. Sornette, 2003. "Renormalization Group Analysis of the 2000-2002 anti-bubble in the US S&P 500 index: Explanation of the hierarchy of 5 crashes and Prediction," Papers physics/0301023, arXiv.org, revised Aug 2003.
    24. Anders Johansen & Didier Sornette, 1999. "Critical Crashes," Papers cond-mat/9901035, arXiv.org.
    25. M. Bartolozzi & S. Drozdz & D. B. Leinweber & J. Speth & A. W. Thomas, 2005. "Self-Similar Log-Periodic Structures in Western Stock Markets from 2000," Papers cond-mat/0501513, arXiv.org, revised Mar 2005.
    26. Zhou, Wei-Xing & Sornette, Didier, 2003. "2000–2003 real estate bubble in the UK but not in the USA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 329(1), pages 249-263.
    27. A. Johansen & D. Sornette, 1999. "Financial ``Anti-Bubbles'': Log-Periodicity in Gold and Nikkei collapses," Papers cond-mat/9901268, arXiv.org.
    28. Zhou, Wei-Xing & Sornette, Didier, 2006. "Is there a real-estate bubble in the US?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 361(1), pages 297-308.
    29. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
    30. Wosnitza, Jan Henrik & Denz, Cornelia, 2013. "Liquidity crisis detection: An application of log-periodic power law structures to default prediction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3666-3681.
    31. Sornette, Didier & Woodard, Ryan & Zhou, Wei-Xing, 2009. "The 2006–2008 oil bubble: Evidence of speculation, and prediction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(8), pages 1571-1576.
    32. Elias G. Carayannis & Aris Kaloudis & åge Mariussen, 2008. "Introduction," Chapters, in: Elias G. Carayannis & Aris Kaloudis & Åge Mariussen (ed.), Diversity in the Knowledge Economy and Society, chapter 1, Edward Elgar Publishing.
    33. J. A. Feigenbaum, 2001. "More on a statistical analysis of log-periodic precursors to financial crashes," Quantitative Finance, Taylor & Francis Journals, vol. 1(5), pages 527-532.
    34. Wosnitza, Jan Henrik & Leker, Jens, 2014. "Why credit risk markets are predestined for exhibiting log-periodic power law structures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 427-449.
    35. George Chang & James Feigenbaum, 2008. "Detecting log-periodicity in a regime-switching model of stock returns," Quantitative Finance, Taylor & Francis Journals, vol. 8(7), pages 723-738.
    36. Didier SORNETTE, 2009. "Dragon-Kings, Black Swans and the Prediction of Crises," Swiss Finance Institute Research Paper Series 09-36, Swiss Finance Institute.
    37. Anders Johansen & Didier Sornette, 2000. "The Nasdaq crash of April 2000: Yet another example of log-periodicity in a speculative bubble ending in a crash," Papers cond-mat/0004263, arXiv.org, revised May 2000.
    38. Drożdż, S. & Grümmer, F. & Ruf, F. & Speth, J., 2003. "Log-periodic self-similarity: an emerging financial law?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 174-182.
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    1. repec:eee:phsmap:v:503:y:2018:i:c:p:947-957 is not listed on IDEAS
    2. Vakhtina, Elena & Wosnitza, Jan Henrik, 2015. "Capital market based warning indicators of bank runs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 417(C), pages 304-320.

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