Detection of Chinese stock market bubbles with LPPLS confidence indicator

We present an advance bubble detection methodology based on the Log Periodic Power Law Singularity (LPPLS) confidence indicator for the early causal identifications of positive and negative bubbles in the Chinese stock market using the daily data on the Shanghai Shenzhen CSI 300 stock market index from January 2002 through April 2018. We account for the damping condition of the LPPLS model in the search space and implement the stricter filter conditions for the qualification of the valid LPPLS fits by considering the maximum relative error, performing the Lomb log-periodic test of the detrended residual, and the unit-root tests of the logarithmic residual based on both the Phillips–Perron test and the Dickey–Fuller test to improve the performance of the LPPLS confidence indicator. Our analysis shows that with forward prediction, the LPPLS detection strategy based on the LPPLS confidence indicator can diagnose both the positive and the negative bubbles corresponding to well-known historical events, demonstrating its outstanding performance to foretell the bubbles in advance. We find that the probability density distribution of the estimated beginning time of bubbles appears to be skewed and the mass of the distribution is concentrated on the area where the price starts to have an obvious super-exponential growth. This study is the first work in literature that identifies the existence of bubbles in the Chinese stock market using the daily data of CSI 300 index with the advance bubble detection methodology of the LPPLS confidence indicator. By forecasting the prospective positive and negative bubbles and their impending crashes ahead of time, one can potentially help limit the bubble sizes and eventually minimize the damages from the bubble crashes.