I remember a thread within the past year (but couldn’t find it) where we discussed the problems of regressions on daily data over different time zones. Axioma has a great white paper on how to do it. http://www.axiomainc.com/newsandresearch/?p=722 Imagine you have Japan and US returns, regress Japan’s return on the lag of US returns, then calculate the predicted series given today’s US returns, then add that to the actual Japan returns. (They had initially used a Vector Autoregression approach constraining everything earlier than when each market closes to 0, but ultimately constrained everything but the US coefficient to 0). I did a preliminary test and it seems to work pretty well, though I would be careful not to use it for things it’s not meant for.