The Twilight Zone (1985)

A researcher from the future, a descendent of President John F. Kennedy goes back in time to witness his ancestor's death, and inadvertently changes history by saving the President. The researcher accidentally gives away the fact that he is from the future, as Kennedy is "pursued" by a series of hurricanes. The researcher soon realizes that he has irrevocably altered history, and there's only one way to fix it. He travels back in time and takes the President's place, leaving his ancestor free to travel back to the future.