By applying two nonlinear Granger causality testing methods and rolling window strategy to explore the relationship between speculative activities and crude oil prices, the unidirectional Granger causality from speculative activities to rets of crude oil prices during the high price phase is discovered. It is proved that speculative activities did contribute to high crude oil prices after the Asian financial crisis and OPEC’s output cut in 1998. The unidirectional Granger causality from rets of crude oil prices to speculative activities is significant in general. But after 2000, with the sharp rise in crude oil prices, this unidirectional Granger causality became a complex nonlinear relationship, which cannot be detected by any linear Granger causality test.