Parapsychology has always taken an avid interest in precognition. There is, however, a parallel phenomenon which, from what I can tell, has not received the same amount of attention, and that is retrocognition.
The most celebrated case is the “timeslip” reported by Annie Moberly and Eleanor Jourdain. But there are other recorded cases.
Assuming, for the same of argument, that this is a genuine phenomenon, then it would undercut the alleged evidence for reincarnation. As one writer explains:
Another method which has been used to induce retrocognition is regression under hypnosis, first explored by Colonel Albert de Rochas around the turn of the century. Subjects could relive what appeared to be episodes in their past lives, he found, though it was rarely possible to verify the episodes, or the lives, historically. Could the explanation be that these were not ‘past lives’ which were being relived, but instances of retrocognition, displaying the confusion familiar in dream precognition? The bulk of the work done with hypnotically regressed subjects, however, has been done in connection with reincarnation, rather than retrocognition, which has largely been ignored by parapsychologists, B. Inglis, The Paranormal: An Encyclopedia of Psychic Phenomena (Paladin 1986), 104.
One might object that this argument is only as good as the alleged evidence for retrocognition. But that argument cuts both ways since we could say exactly the same thing about reincarnation.