I'm not very fluent in the quant vernacular, so perhaps the nature of my question will be better illustrated as a hypothesis.
One market has closed and another market elsewhere on Spaceship Earth is opening. For example, the Nikkei opens at 7pm Eastern time, a few hours after NYSE has closed. Let's hypothesize that there's a higher demand for JPY from USD holders during this interval than any other interval during the day, and consequently there is a greater probability of profiting from a buy & sell of JPY during this interval than other intra-day interval.
What kind of statistical analysis would you do to test this hypothesis?