  We introduce the concept of "negative bubbles" as the mirror image of
standard financial bubbles, in which positive feedback mechanisms may lead to
transient accelerating price falls. To model these negative bubbles, we adapt
the Johansen-Ledoit-Sornette (JLS) model of rational expectation bubbles with a
hazard rate describing the collective buying pressure of noise traders. The
price fall occurring during a transient negative bubble can be interpreted as
an effective random downpayment that rational agents accept to pay in the hope
of profiting from the expected occurrence of a possible rally. We validate the
model by showing that it has significant predictive power in identifying the
times of major market rebounds. This result is obtained by using a general
pattern recognition method which combines the information obtained at multiple
times from a dynamical calibration of the JLS model. Error diagrams, Bayesian
inference and trading strategies suggest that one can extract genuine
information and obtain real skill from the calibration of negative bubbles with
the JLS model. We conclude that negative bubbles are in general predictably
associated with large rebounds or rallies, which are the mirror images of the
crashes terminating standard bubbles.
