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This paper explores nonlinear cointegration between Chinese mainland stock markets and Hong Kong stock market in a multivariate framework for the period January, 1998 to December, 2014 by a nonparametric method. The local linear kernel smoothing method is developed to estimate the unknown function, and the practical problem of implementation is also addressed. Then, a simple nonparametric version of a bootstrap test is adapted for testing misspecification. Furthermore, Some Monte Carlo experiments are presented to examine the finite sample performance of the proposed procedure. Finally, the stock markets data set is discussed in detail by using proposed procedures, showing that Shanghai Stock Index (SHSI) and Shenzhen Component Index (SZCI) can affect Hang Seng Index (HSI), and the influence appears to be a strong nonlinear characteristics.

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