Testing for Multiple Bubbles: Historical Episodes of Exuberance and Collapse in the S&P 500

Peter C. B. PHILLIPS, Singapore Management University
Shuping SHI
Jun YU, Singapore Management University


Recent work on econometric detection mechanisms has shown the effectiveness of recursive procedures in identifying and dating financial bubbles in real time. These procedures are useful as warning alerts in surveillance strategies conducted by central banks and fiscal regulators with real-time data. Use of these methods over long historical periods presents a more serious econometric challenge due to the complexity of the nonlinear structure and break mechanisms that are inherent in multiple-bubble phenomena within the same sample period. To meet this challenge, this article develops a new recursive flexible window method that is better suited for practical implementation with long historical time series. The method is a generalized version of the sup augmented Dickey-Fuller (ADF) test of Phillips etal. (Explosive behavior in the 1990s NASDAQ: When did exuberance escalate asset values? International Economic Review 52 (2011), 201-26; PWY) and delivers a consistent real-time date-stamping strategy for the origination and termination of multiple bubbles. Simulations show that the test significantly improves discriminatory power and leads to distinct power gains when multiple bubbles occur. An empirical application of the methodology is conducted on S&P 500 stock market data over a long historical period from January 1871 to December 2010. The new approach successfully identifies the well-known historical episodes of exuberance and collapses over this period, whereas the strategy of PWY and a related cumulative sum (CUSUM) dating procedure locate far fewer episodes in the same sample range.