If your any pointing device driver is outdated or corrupted, it would cause your mouse cursor keeps moving on its own. It can fix the problem through updating your pointing device driver, like mouse, keyboard and touchpad driver. ... Driver Easy will automatically recognize your system and find the correct drivers for it.

Also, I had a similar issue a few years ago when I used as mouse pad a white cardboard. White color was the reason at that time and the solution was to replace the pad with a colored one.