Rational speculative bubble size in Hang Seng, S&P500 and Nikkei 225 index trend from year 1976 until 2016

Rational speculative bubble size happens when the prices of an asset surpass its intrinsic value. This bubbles are harmful when burst because its gives a big impact towards the economic. The aims of this study is to show the size of rational speculative bubble existed from year 1976 until 2016. The period are separated into four which are the first cycle is from 1/11976 to 6/12/1987, the second cycle happen in 7/12/1987 to 12/8/1998, 13/8/1998 to 26/10/2008 for the third cycle and 27/10/2008 to 31/12/2016 for the fourth cycle. This study is also emphasizing on the trend of the rational speculative bubble from one cycle to another cycle. This bubbles size was studied in three markets which are Hang Seng, S&P 500 and Nikkei 225 by using generalized Johansen-Ledoit-Sornette model.