This paper apply ESTAR model on the empirical study of the Hong Kong Hengseng stock-index 933 , 9312 , 943 and S&P 500 stock-index 933 , 9312 , 943 , and the study result is that the price of Hong Kong Hengseng stock-index 933 , 9312 appear the nonlinear characteristic , but others appear the linear characteristic. Accordingly , we can get such conclusion : the absence of stock short system makes the arbitrage cost bigger and restrains the de2 velopment of the arbitrage. Under such market , the price of the stock-index appears the nonlinear characteristics. However , the chance of unilateral arbitrage under such market is more than that in the developed market