Prediction Accuracy and Sloppiness of Log-Periodic Functions

6 Pages Posted: 24 Jun 2010

See all articles by David Brée

David Brée

University of Manchester - School of Computer Science

Damien Challet

CentraleSupélec; Encelade Capital SA

Pier Paolo Peirano

Capital Fund Management

Date Written: June 23, 2010

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 predictability of 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.

Keywords: bubbles, crash, prediction, log-periodic fits

JEL Classification: G12, G14

Suggested Citation

Brée, David and Challet, Damien and Peirano, Pier Paolo, Prediction Accuracy and Sloppiness of Log-Periodic Functions (June 23, 2010). Available at SSRN: https://ssrn.com/abstract=1629363 or http://dx.doi.org/10.2139/ssrn.1629363

David Brée

University of Manchester - School of Computer Science ( email )

Kilburn Building, Oxford Road
Manchester M13 9GH, M13 9PL
United Kingdom

Damien Challet (Contact Author)

CentraleSupélec ( email )

Labo MICS
3, rue Joliot-Curie
Gif-sur-Yvette, 91192
France

Encelade Capital SA ( email )

Chemin du Bochet 8
Sulpice, 1025
Switzerland

Pier Paolo Peirano

Capital Fund Management ( email )

23 rue de l'Université
Paris, 75007
France

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