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Prediction accuracy and sloppiness of log-periodic functions

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  • David S. Br�e
  • Damien Challet
  • Pier Paolo Peirano

Abstract

We show that log-periodic power-law (LPPL) functions are intrinsically very hard to fit to time series. This comes from their sloppiness, the squared residuals depending very much on some combinations of parameters and very little on other ones. The time of singularity that is supposed to give an estimate of the day of the crash belongs to the latter category. We discuss in detail why and how the fitting procedure must take into account the sloppy nature of this kind of model. We then test the reliability of LPPLs on synthetic AR(1) data replicating the Hang Seng 1987 crash and show that even this case is borderline regarding the predictability of the divergence time. We finally argue that current methods used to estimate a probabilistic time window for the divergence time are likely to be over-optimistic.

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  • David S. Br�e & Damien Challet & Pier Paolo Peirano, 2013. "Prediction accuracy and sloppiness of log-periodic functions," Quantitative Finance, Taylor & Francis Journals, vol. 13(2), pages 275-280, January.
    • Handle: RePEc:taf:quantf:v:13:y:2013:i:2:p:275-280
    DOI: 10.1080/14697688.2011.607467
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    1. Stanislaw Drozdz & Jaroslaw Kwapien & Pawel Oswiecimka & Josef Speth, 2008. "Current log-periodic view on future world market development," Papers 0802.4043, arXiv.org, revised Jun 2008.
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    Cited by:

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    5. Fry, John, 2012. "Exogenous and endogenous crashes as phase transitions in complex financial systems," MPRA Paper 36202, University Library of Munich, Germany.
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    10. 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.
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