Dissecting the 2015 Chinese stock market crash

We perform a novel analysis of the 2015 Chinese stock market crash by calibrating the log-periodic power law singularity (LPPLS) model to two important Chinese stock indices, SSEC and SZSC, from early 2014 to June 2015. Our analysis indicates that the LPPLS model can readily detect the bubble behaviour of the faster-thanexponential increase corrected by the accelerating logarithm-periodic oscillations in the crash. The existence of the log-periodicity is identified by applying the Lomb spectral analysis on the detrended residuals. The Ornstein-Uhlenbeck property and the stationarity of the LPPLS fitting residuals are confirmed by the Phillips-Perron test and the Dickey-Fuller test. We find that the actual critical day t(c) of bubble crash can be well predicted by the LPPLS model as far back as 2 months before the actual crash. We have shown that the covariance matrix adaptation evolution strategy (CMA-ES) can be used as an alternative optimization algorithm for the LPPLS model fit. Furthermore, the change rate of the prediction end time gap (t(c) - t(2)) can be used as an additional indicator along with the key indicator t(c) to improve the prediction of bubble burst.