Identifying explosive bubbles that are characterized by periodically collapsing behavior over time has been a major concern in the literature and is of great importance for practi-tioners. The complexity of the nonlinear structure in multiple bubble phenomena diminishes the discriminatory power of existing tests, as evidenced in early simulations conducted by Evans (1991). Multiple collapsing bubble episodes within the same sample period make bubble diagnosis particularly di ¢ cult and complicate attempts at econometric dating. The present paper systematically investigates these issues and develops new procedures for prac-tical implementation and surveillance strategies by central banks. We show how the testing procedure and dating algorith...