Eur. Phys. J. B 61, 355-362 (2008)
https://doi.org/10.1140/epjb/e2008-00085-1

The log-periodic-AR(1)-GARCH(1,1) model for financial crashes

¹ Departamento de Engenharia Elétrica, Pontifícia Universidade Católica do Rio de Janeiro, 22453-900 Rio de Janeiro, RJ, Brasil
² Instituto de Gestão de Riscos Financeiros e Atuariais (IAPUC), Pontifícia Universidade Católica do Rio de Janeiro, 22453-900 Rio de Janeiro, RJ, Brasil
³ Departamento de Física, Pontifícia Universidade Católica do Rio de Janeiro, 22453-900 Rio de Janeiro, RJ, Brasil

Corresponding author: ^a rrif@fis.puc-rio.br

Received: 3 September 2007
Revised: 2 November 2007
Published online: 29 February 2008

Abstract

This paper intends to meet recent claims for the attainment of more rigorous statistical methodology within the econophysics literature. To this end, we consider an econometric approach to investigate the outcomes of the log-periodic model of price movements, which has been largely used to forecast financial crashes. In order to accomplish reliable statistical inference for unknown parameters, we incorporate an autoregressive dynamic and a conditional heteroskedasticity structure in the error term of the original model, yielding the log-periodic-AR(1)-GARCH(1,1) model. Both the original and the extended models are fitted to financial indices of U. S. market, namely S&P500 and NASDAQ. Our analysis reveal two main points: (i) the log-periodic-AR(1)-GARCH(1,1) model has residuals with better statistical properties and (ii) the estimation of the parameter concerning the time of the financial crash has been improved.