Eur. Phys. J. B (2014) 87: 228
https://doi.org/10.1140/epjb/e2014-41085-6

Regular Article

Bayesian log-periodic model for financial crashes

Center for Research in Econometric Analysis of Time Series (CREATES) and Department of Economics and Business, Aarhus University, Fuglesangs Allé 4, Building 2622 (203), 8210 Aarhus V, Denmark

^a e-mail: vrodriguez@creates.au.dk

Received: 18 December 2013
Received in final form: 3 August 2014
Published online: 7 October 2014

Abstract

This paper introduces a Bayesian approach in econophysics literature about financial bubbles in order to estimate the most probable time for a financial crash to occur. To this end, we propose using noninformative prior distributions to obtain posterior distributions. Since these distributions cannot be performed analytically, we develop a Markov Chain Monte Carlo algorithm to draw from posterior distributions. We consider three Bayesian models that involve normal and Student’s t-distributions in the disturbances and an AR(1)-GARCH(1,1) structure only within the first case. In the empirical part of the study, we analyze a well-known example of financial bubble – the S&P 500 1987 crash – to show the usefulness of the three methods under consideration and crashes of Merval-94, Bovespa-97, IPCMX-94, Hang Seng-97 using the simplest method. The novelty of this research is that the Bayesian models provide 95% credible intervals for the estimated crash time.