Detecting bubbles via FDR and FNR based on calibrated <i>p</i> -values

Detecting bubbles in asset prices is still an open question that has attracted considerable attention in recent years. This paper improves the bubble detection and dating approaches developed in recent years by Phillips and co-authors, proposing to assess the plausibility of its outcomes via the false discovery rate (FDR) and the false non-discovery rate (FNR) based on calibrated p-values. Calibrating p-values of unit root tests, applied sequentially to detect bubbles, allows recovery of their super-uniformity property, which is crucial for a valid implementation of the inferential procedure. The paper also develops original self-calibrated versions of both FDR and FNR for the specific problem of bubble testing. Calibrated p-values are implemented in an online false discovery-based approach which monitors bubbles in real time. The effectiveness of the proposed methods is investigated via a simulation study and an empirical application.