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This research empirically examines whether the emergence of China and its monetary policy have caused cross-border influences upon the main global stock markets, including the markets in advanced and emerging economies. We argue that since the stock market fluctuates constantly with structural breaks, the cointegration test should be able to characterize this feature when testing the effect from monetary policy to the stock market. The empirical literature using the traditional cointegration approach often presents mixed conclusions on the relationship between stock markets and monetary policy. To justify this argument, we propose a residual-based single-equation cointegration approach in which variables are cointegrated with smoothing regime shifts in order to characterize the presence of structural breaks for stock market. As it is difficult to precisely estimate the number and magnitudes of multiple breaks by the dummy variables approach, the new cointegration approach utilizes a flexible Fourier function to take into account smoothing breaks. By adopting the new approach, we are able to offer evidence for the long-run cointegration between China's monetary policy and each of the selected global stock market. We find that, by adopting the new approach, China's monetary policy delivers international policy transmission to the stock markets of newly developed and emerging economies (NDEE) yet not to the stock markets of the main advanced economies. In addition, the empirical results are robust across policy variables. [ABSTRACT FROM AUTHOR]