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In this study, we perform a novel analysis of the 2015 financial bubble inthe Chinese stock market by calibrating the Log Periodic Power Law Singularity(LPPLS) model to two important Chinese stock indices, SSEC and SZSC, from early2014 to June 2015. The back tests of the 2015 Chinese stock market bubblesindicates that the LPPLS model can readily detect the bubble behavior of thefaster-than-exponential increase corrected by the acceleratinglogarithm-periodic oscillations in the 2015 Chinese Stock market. The existenceof log-periodicity is detected by applying the Lomb spectral analysis on thedetrended residuals. The Ornstein-Uhlenbeck property and the stationarity ofthe LPPLS fitting residuals are confirmed by the two Unit-root tests(Philips-Perron test and Dickery-Fuller test). According to our analysis, theactual critical day t_c can be well predicted by the LPPLS model as far back astwo months before the actual bubble crash. Compared to the traditionaloptimization method used in the LPPLS model, we find the covariance matrixadaptation evolution strategy (CMA-ES) to have a significantly lowercomputation cost, and thus recommend this as a better alternative algorithm forLPPLS model fit. Furthermore, in the LPPLS fitting with expanding windows, thegap (tc -t2) shows a significant decrease when the end day t2 approaches theactual bubble crash time. The change rate of the gap (tc-t2) may be used as anadditional indicator besides the key indicator tc to improve the prediction ofbubble burst.

Diagnosis and Prediction of the 2015 Chinese Stock Market Bubble