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Detecting log-periodicity in a regime-switching model of stock returns

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  • George Chang
  • James Feigenbaum

Abstract

Log-periodic precursors have been identified before most and perhaps all financial crashes of the Twentieth Century, but efforts to statistically validate the leading model of log-periodicity, the Johansen-Ledoit-Sornette (JLS) model, have generally failed. The main feature of this model is that log-harmonic fluctuations in financial prices are driven by similar fluctuations in expected daily returns. Here we search more broadly for evidence of any log-periodic variation in expected daily returns by estimating a regime-switching model of stock returns in which the mean return fluctuates between a high and a low value. We find such evidence prior to the two largest drawdowns in the S&P 500 since 1950. However, if we estimate a log-harmonic specification for the stock index for the same time periods, fixing the frequency and critical time according to the results of the regime-switching model, the parameters do not satisfy restrictions imposed by the JLS model.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:quantf:v:8:y:2008:i:7:p:723-738
    DOI: 10.1080/14697680701689620
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    References listed on IDEAS

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    1. Levy, Haim & Levy, Moshe & Solomon, Sorin, 2000. "Microscopic Simulation of Financial Markets," Elsevier Monographs, Elsevier, edition 1, number 9780124458901.
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    Citations

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    Cited by:

    1. Fry, J. M., 2010. "Gaussian and non-Gaussian models for financial bubbles via econophysics," MPRA Paper 27307, University Library of Munich, Germany.
    2. Giacomo Bormetti & Maria Elena De Giuli & Danilo Delpini & Claudia Tarantola, 2008. "Bayesian Analysis of Value-at-Risk with Product Partition Models," Papers 0809.0241, arXiv.org, revised May 2009.
    3. Fry, J. M., 2009. "Statistical modelling of financial crashes: Rapid growth, illusion of certainty and contagion," MPRA Paper 16027, University Library of Munich, Germany.
    4. Pawel Dlotko & Simon Rudkin, 2019. "The Topology of Time Series: Improving Recession Forecasting from Yield Spreads," Working Papers 2019-02, Swansea University, School of Management.
    5. Fry, John, 2012. "Exogenous and endogenous crashes as phase transitions in complex financial systems," MPRA Paper 36202, University Library of Munich, Germany.
    6. Sornette, Didier & Woodard, Ryan & Yan, Wanfeng & Zhou, Wei-Xing, 2013. "Clarifications to questions and criticisms on the Johansen–Ledoit–Sornette financial bubble model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(19), pages 4417-4428.
    7. John Fry & McMillan David, 2015. "Stochastic modelling for financial bubbles and policy," Cogent Economics & Finance, Taylor & Francis Journals, vol. 3(1), pages 1002152-100, December.
    8. Fry, J. M., 2010. "Bubbles and crashes in finance: A phase transition from random to deterministic behaviour in prices," MPRA Paper 24778, University Library of Munich, Germany.
    9. John Fry, 2014. "Bubbles, shocks and elementary technical trading strategies," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 87(1), pages 1-13, January.
    10. Hsu, Yuan-Lin & Lin, Shih-Kuei & Hung, Ming-Chin & Huang, Tzu-Hui, 2016. "Empirical analysis of stock indices under a regime-switching model with dependent jump size risks," Economic Modelling, Elsevier, vol. 54(C), pages 260-275.
    11. Fry, J. M., 2009. "Bubbles and contagion in English house prices," MPRA Paper 17687, University Library of Munich, Germany.
    12. Giacomo Bormetti & Maria Elena De Giuli & Danilo Delpini & Claudia Tarantola, 2012. "Bayesian Value-at-Risk with product partition models," Quantitative Finance, Taylor & Francis Journals, vol. 12(5), pages 769-780, November.
    13. 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.
    14. 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.
    15. Filimonov, V. & Sornette, D., 2013. "A stable and robust calibration scheme of the log-periodic power law model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3698-3707.

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