  Establishing unambiguously the existence of speculative bubbles is an
on-going controversy complicated by the need of defining a model of fundamental
prices. Here, we present a novel empirical method which bypasses all the
difficulties of the previous approaches by monitoring external indicators of an
anomalously growing interest in the public at times of bubbles. From the
definition of a bubble as a self-fulfilling reinforcing price change, we
identify indicators of a possible self-reinforcing imitation between agents in
the market. We show that during the build-up phase of a bubble, there is a
growing interest in the public for the commodity in question, whether it
consists in stocks, diamonds or coins. That interest can be estimated through
different indicators: increase in the number of books published on the topic,
increase in the subscriptions to specialized journals. Moreover, the well-known
empirical rule according to which the volume of sales is growing during a bull
market finds a natural interpretation in this framework: sales increases in
fact reveal and pinpoint the progress of the bubble's diffusion throughout
society. We also present a simple model of rational expectation which maps
exactly onto the Ising model on a random graph. The indicators are then
interpreted as ``thermometers'', measuring the balance between idiosyncratic
information (noise temperature) and imitation (coupling) strength. In this
context, bubbles are interpreted as low or critical temperature phases, where
the imitation strength carries market prices up essentially independently of
fundamentals. Contrary to the naive conception of a bubble and a crash as times
of disorder, on the contrary, we show that bubbles and crashes are times where
the concensus is too strong.

Statistical Mechanics;General Finance