Sequential Detector Statistics for Speculative Bubbles

Abstract

We propose a heteroskedasticity-robust locally best invariant (LBI) statistic to test the hypothesis of a unit root against the alternative of an explosive root associated with speculative bubbles. Compared to existing alternatives such as Dickey-Fuller type tests, the LBI statistic has a standard limiting distribution and greater power, particularly in the empirically relevant scenario of a moderately explosive root. Further refinements, such as the point-optimal linear test, approach the power envelope remarkably closely. To detect bubbles with an unknown starting date, we consider sequential (CUSUM) schemes based on constant and time-varying boundary functions, where the exponentially weighted CUSUM detector with a constant boundary function turns out to be most powerful. We also propose a simple method for date-stamping the start of the bubble consistently. Finally, we illustrate our methods using two empirical examples.