  By combining (i) the economic theory of rational expectation bubbles, (ii)
behavioral finance on imitation and herding of investors and traders and (iii)
the mathematical and statistical physics of bifurcations and phase transitions,
the log-periodic power law model has been developed as a flexible tool to
detect bubbles. The LPPL model considers the faster-than-exponential (power law
with finite-time singularity) increase in asset prices decorated by
accelerating oscillations as the main diagnostic of bubbles. It embodies a
positive feedback loop of higher return anticipations competing with negative
feedback spirals of crash expectations. We use the LPPL model in one of its
incarnations to analyze two bubbles and subsequent market crashes in two
important indexes in the Chinese stock markets between May 2005 and July 2009.
Both the Shanghai Stock Exchange Composite and Shenzhen Stock Exchange
Component indexes exhibited such behavior in two distinct time periods: 1) from
mid-2005, bursting in Oct. 2007 and 2) from Nov. 2008, bursting in the
beginning of Aug. 2009. We successfully predicted time windows for both crashes
in advance with the same methods used to successfully predict the peak in
mid-2006 of the US housing bubble and the peak in July 2008 of the global oil
bubble. The more recent bubble in the Chinese indexes was detected and its end
or change of regime was predicted independently by two groups with similar
results, showing that the model has been well-documented and can be replicated
by industrial practitioners. Here we present more detailed analysis of the
individual Chinese index predictions and of the methods used to make and test
them.
