“…Figure 2a implies that the gradient of exponential growth and the frequency of log-periodic oscillation are increasing. Furthermore, using the German stock index, Kurz-Kim [51] provided empirical evidence of the imminence of critical time, in which the gradient of exponential growth increases from 0.27%, to 0.67%, to 1.70%, to 4.29%, to 12.9%, while the period of log-periodic oscillation decreases by 60% in each interval from 255, to 102, to 41, to 16, to 7 trading days. Our analysis notes that the exponential growth rate is greater than 0.27%, i.e., 0.1% and 0.59% at the second and third peaks, respectively, and is about to enter the second stage of the example in Reference [51].…”