This paper analyzes the multivariate volatility effects among the indexes returns time series of the main stock markets. We detect, applying cointegration techniques, relations of interdependence between these markets and the existence of structural changes. Next, we study the behaviour of volatility with the O-GARCH model and how the frequency affects the dynamics of volatility. The results show that the estimated breakpoints are related to the dates of high volatility; therefore the volatility of financial markets affects long term financial relationships. Finally, we conclude that the low frequency data are useful for the study of cointegration relation-ships, though the estimation of volatility requires high frequency data.