A recursive test procedure is suggested that provides a mechanism for testing explosive behavior, date-stamping the origination and collapse of economic exuberance, and providing valid conﬁdence intervals for explosive growth rates. The method involves the recursive implementation of a right-side unit root test and a sup test, both of which are easy to use in practical applications, and some new limit theory for mildly explosive processes. The test procedure is shown to have discriminatory power in detecting periodically collapsing bubbles, thereby overcoming a weakness in earlier applications of unit root tests for economic bubbles. An empirical application to Nasdaq stock price index in the 1990s provides conﬁrmation of explosiveness and date-stamps the origination of ﬁnancial exuberance to mid -1995, prior to the famous remark in December 1996 by Alan Greenspan about irrational exuberance in ﬁnancial markets, thereby giving the remark empirical content.
Phillips, Peter C.B.; Wu, Yangru; and Yu, Jun, "Explosive Behavior in the 1990s Nasdaq: When Did Exuberance Escalate Asset Values?" (2009). Cowles Foundation Discussion Papers. 2017.