Comparing the Supremum Augmented Dickey Fuller and Log Periodic Power Law Frameworks for Identifying Bubbles

Abstract

This paper compares the ability of the log periodic power law (LPPL) procedure and the supremum augmented Dickey Fuller (supremum ADF) tests to confirm or reject the presence of bubbles in various time series simulations. We develop a time stamping method for the LPPL procedure and derive a more general formulation allowing for non-zero required rate of return. We support earlier findings that the standard generalized SADF test is oversized when subject to serially correlated innovations, and that this can be helped by bootstrapping the critical value distribution. Furthermore, we document that both the standard and the bootstrap GSADF test suffer from oversized test statistics when subject to GARCH innovations. The LPPL procedure shows promising results but these are highly dependent on its specific formulation.

Keywords: rational bubbles, explosive processes, log periodic power law, critical points theory

JEL Classification: C01, C02, C12, C13, C22, C52, C53, C58, C61, G01