Before revision:  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 bubbles start to have a super-exponentially growth.
After revision:  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-exponentially growth.