This paper uses stochastic-parameter regressions to analyze the role of foreign information on the return equivalent of the heat wave and meteor shower hypotheses of Engle etal. [Engle, R.F., Ito, T., Lin, W., 1990 Meteor showers or heat waves? Heteroscedastic intra-daily volatility in the foreign exchange market. Econometrica 59, 525-542]. The impact of foreign information on the level and intensity of signal transmission within and between international stock markets is assessed. It is found that signals are transmitted directly from some markets to others and indirectly through other markets. Transmission across regions is stronger than within regions, but most relationships vary over time. Foreign information plays an important role, and can be used profitably in out-of-sample trading, but some stock markets are immune to the effect of information from others.