Peculiar statistical properties of Chinese stock indices in bull and bear market phases

Chinese stock markets have experienced an extraordinary bull market since Jan 2006, which attracted global eyes. We investigate the statistical properties of the indices’ log-return r(t) for the bull market (Jan 2006–Oct 2007) and the previous bear market (Jan 2001–Dec 2005). Here we report three peculiar features of r(t): (i) the cumulative distribution function curve of r(t) in the bull market is similar to that in the bear market; (ii) the autocorrelation function of r(t) in the bull market has a stronger negative correlation and a shorter correlation time than that in the bear market; (iii) the bull market shows stronger long-term correlation than the bear market. This work has relevance to understanding novel statistical properties in economic systems.