FAQ/One Axis Stabilization

From VFXPedia

Connect your footage to a Transform, then modify the Transform's Center with the Expression modifier (RMB>Modify With>Expression). In the Expression connect Point in 1 to the tracker and type 0.5 in Point Out>Point Expression X, type p1y in Point Out>Point Expression Y.

You can also use a Simple Expression:
RMB on the Transform's Center>Expression
In the row that's appeared below enter: Point(0.5, Tracker.UnsteadyPosition.Y)
--Gringo

If you want to have even more control of a tracker's X and Y positions, there are two scripts on VFXpedia that can convert a displacement path into an XY path:

Tracker to Transform and Convert Path to XY Path