Testing for Periodically Collapsing Bubbles: an Generalized Sup Adf Test

Identifying explosive bubbles under the influence of their periodically collapsing property has long been a concern in bubble testing literature. In this paper, we argue that the sup Augmented Dickey-Fuller (ADF) test (Phillips, Wu and Yu, 2009), which implements a right-tail ADF test and a sup test on a forward expanding sample sequence, is sensitive to the sample starting point when there are more than one bubble collapsing episodes within the sample range. To surmount this pitfall we propose an alternative method named the generalized sup ADF test, which amplifies the sample sequence by varying the sample starting point within its feasible range. This test improves the power of the bubble testing method significantly. We then apply both tests to the Hong Kong stock market from October 1980 to April 2009. The generalized sup ADF tests find evidence of explosive behavior in the Hang Seng Index, whereas the sup ADF tests suggest the opposite.