Fluctuation-type monitoring test for explosive behavior

Abstract

A fluctuation-type monitoring test for a bubble is proposed. The initial value is dealt with by either OLS or quasi-difference demeaning. The asymptotic property of the test under mildly explosive and local alternatives is investigated. It is shown that the fluctuation-type test has an advantage over the existing methods when the bubble appears mid- to late in the monitoring period or the bubble period is relatively long, whereas the CUSUM monitoring scheme performs better in view of power for an early bubble in the monitoring period. This theoretical property is supported in finite samples by Monte Carlo simulations. As none of the existing tests uniformly outperforms the others, the union of rejections strategy by combining the two or three monitoring tests is also proposed, which is shown to work well in finite samples.