Informational Criteria for Positive and Negative Bubbles: An Experiment in Forensic Finance

Abstract

The notion of bubbles is ubiquitous in the public discussion of finance. Yet, the empirical discovery of bubbles is notoriously difficult. The main shortcoming of the current approaches is that they rely on the estimation of the “fundamental value of an asset”, which is hard to estimate and interpret. In 2006-2007, Jarrow, Protter and Shimbo (JPS) proposed another approach to bubbles, one, which does not rely on the notion of the fundamental value of an asset. In 2008, the author developed two hypotheses (or theorems) connecting the JPS approach with the serial correlations in returns of specially designed assets. These hypotheses were tested by the author on a proverbial example of the Nasdaq index in 1999-2001 — the time of a hypothetical dot-com bubble. By this work, I continue this study by applying informational criteria to the cases of a sharp drop in oil prices in the end of 1980s and the beginning of 1990s. The sharp drop in oil prices can indicate unknown fundamental factors in oil prices, or a negative bubble. While the application of JPS theory to negative bubbles is tenuous, a sheer possibility that the subject of a negative bubble can be empirically studied for commodities, offers a fascinating glimpse into the market behavior.