We investigate spatial and temporal cross-correlations between streamwise and normal velocity components in three shear flows: a low-dimensional model for vortex–streak interactions, direct numerical simulations for a nearly homogeneous shear flow and experimental data for a turbulent boundary layer. Driving of streamwise streaks by streamwise vortices gives rise to a temporal asymmetry in the short-time correlation. Close to the wall or the bounding surface in the free-slip situations, this asymmetry is identified. Further away from the boundaries the asymmetry becomes weaker and changes character, indicating the prevalence of other processes. The systematic variation of the asymmetry measure may be used as a complementary indicator to separate different layers in turbulent shear flows. The location of the extrema at different streamwise displacements can be used to read off the mean advection speed; it differs from the mean streamwise velocity because of asymmetries in the normal extent of the structures.