Bubbles and the Weibull distribution: was there an explosive bubble in US stock prices before the global economic crisis?

Abstract

Existing studies on bubbles have been mainly concerned with investigating the stationarity properties of stock prices and market fundamentals. We develop a new method of testing for bubbles that relates the bubble component of stock prices to the probability of bursting in the context of the Weibull distribution. There were several eruptions and subsequent collapses of seeming bubbles over the past three decades: 1987 (Black Monday), 2000 (information technology (IT) boom) and 2007 (housing market boom). Using US monthly data for the S&P 500 and NASDAQ series, we have found that the S&P 500 series contained an explosive bubble only during the boom of the housing market that occurred before the 2007 global economic crisis, and the NASDAQ market contained an explosive bubble during the surge of stock prices peaking in 1987 and 2007, although our stationarity tests fail to detect the bubbles. No bubble was found in both the S&P and NASDAQ series during the 2000 IT boom. Our evidence corroborates the criticism that the traditional unit root and cointegration tests may not be able to detect some important class of bubbles.