Any "change" in the past is inherently paradoxical (to say the least). In fact, I think it is actually worse than that: Such changes would involve making it both true and false in the history of our world that the changed event did (or did not) take place. That's a contradiction, not a paradox.
On the other hand, one could go back in time and do what one actually did in some time long past (or do what one actually will do, some time long in the future). If it is actually possible to go back in time, for example, and be one's own father, then one would live in a universe in which that is (and always was) precisely what happened. What are called "looping" universes, in which time did not flow linearly, but in a closed loop, would make such apparently strange events possible. And though we have good reasons for supposing that we do not live in a looping universe, it does not seem that logic makes such an idea impossible.
To find out more about this topic, have a look at an article by David Lewis entitled "The Paradoxes of Time Travel" which was published in the American Philosophical Quarterly, vol. 13 (1976), 145-152. Lewis also cites two stories by Robert Heinlein in which the picture of time travel that he develops appear to be assumed.