In this study, we apply directed acyclic graphs and search algorithm designed for time series with non-Gaussian distribution to obtain causal structure of innovations from an error correction model. The structure of interdependencies among six international stock markets is investigated. The results provide positive empirical evidence that there exist long-run equilibrium and contemporaneous causal structure among these stock markets. DAG analysis results show that Hong Kong is influenced by all other open markets in contemporaneous time, whereas Shanghai is not influenced by any of the other markets in contemporaneous time. Historical decompositions indicate that New York and Shanghai stock markets are highly exogenous and Germany and Hong Kong are the least exogenous markets. Further, we find that New York is the most influential stock market with consistent impact on price movements. One implication is that diversification between US and Germany may not provide desired immunity from financial crisis contagion as much as it does diversification between US and Shanghai.