How to implement time traveling into a game?

I was wondering how to implement time travel into a game. Nothing super complex, just time-reversal like what's in Braid, where the user can rewind/fast forward time by 30 seconds or whatever.

I searched around the web a lot, but my results usually referred to using time as in like "it's 3:00" or a timer and such.

The only thing I could think of was using 2 arrays, one for the player's x position and the other for the player's y position, and then iterating through those arrays and placing the character at that position as they rewind/fast forward time. Could that work? If it would work, how large would the array have to be and how often should I store the player's x and y? If it doesn't work, what else could I try?

Thanks in advance!