It tends to start moving in the 1am to 3am range. When it gets going it seems to trend for a long time. Trend following strategies seem to work better during these light volume hours.
If you trade the ES from 3:00 AM to 9:00 AM EST (9:00 AM to 3:00 PM Central European Time) you have to watch the DAX and the FTSE and be aware of the time of scheduled European economic reports.