In Singularity or Bust I discussed the work of econophysicist Didier Sornette et al in using oscillating hyperexponentials to predict the collapse of Chinese equity markets. They have a new paper out which tells a bit more about how they predict the point of collapse. H/t Physics arXiv Blog.
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 (LPPL) 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 be-
tween May 2005 and July 2009. Both the Shanghai Stock Exchange Composite index (US ticker symbol SSEC) and
Shenzhen Stock Exchange Component index (SZSC) exhibited such behavior in two distinct time periods: 1) from
mid-2005, bursting in October 2007 and 2) from November 2008, bursting in the beginning of August 2009. We
successfully predicted time windows for both crashes in advance [24, 1] 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 indepen-
dently 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. We complement the detection of log-periodic behavior with Lomb spectral
analysis of detrended residuals and (H, q)-derivative of logarithmic indexes for both bubbles. We perform unit-root
tests on the residuals from the log-periodic power law model to conﬁrm the Ornstein-Uhlenbeck property of bounded
residuals, in agreement with the consistent model of ‘explosive’ ﬁnancial bubbles .