Previous studies on cointegration among national stock markets show conflicting results. This paper designs a general state space model to investigate the importance of a common world-wide component and the existence of country-specific components in national stock market indices. For G7 countries, there exist country-specific permanent and transitory components. Based on a variance decomposition analysis, Germany, Italy, and Japan's country-specific permanent shocks account for about half of their total permanent shocks. Most of France, Germany, and the United Kingdom's transitory shocks are country-specific. G7 countries do not seem to cointegrate around one common stochastic trend, and potential long-run international diversification benefits still exist.