  We introduce the Speculative Influence Network (SIN) to decipher the causal
relationships between sectors (and/or firms) during financial bubbles. The SIN
is constructed in two steps. First, we develop a Hidden Markov Model (HMM) of
regime-switching between a normal market phase represented by a geometric
Brownian motion (GBM) and a bubble regime represented by the stochastic
super-exponential Sornette-Andersen (2002) bubble model. The calibration of the
HMM provides the probability at each time for a given security to be in the
bubble regime. Conditional on two assets being qualified in the bubble regime,
we then use the transfer entropy to quantify the influence of the returns of
one asset $i$ onto another asset $j$, from which we introduce the adjacency
matrix of the SIN among securities. We apply our technology to the Chinese
stock market during the period 2005-2008, during which a normal phase was
followed by a spectacular bubble ending in a massive correction. We introduce
the Net Speculative Influence Intensity (NSII) variable as the difference
between the transfer entropies from $i$ to $j$ and from $j$ to $i$, which is
used in a series of rank ordered regressions to predict the maximum loss
(\%{MaxLoss}) endured during the crash. The sectors that influenced other
sectors the most are found to have the largest losses. There is a clear
prediction skill obtained by using the transfer entropy involving industrial
sectors to explain the \%{MaxLoss} of financial institutions but not vice
versa. We also show that the bubble state variable calibrated on the Chinese
market data corresponds well to the regimes when the market exhibits a strong
price acceleration followed by clear change of price regimes. Our results
suggest that SIN may contribute significant skill to the development of general
linkage-based systemic risks measures and early warning metrics.
