This week's episode of Game of Thrones saw Bran tragically turn young Wyllis into Hodor, confirming the idea that he can affect events in the past.
As Reddit user Jdylopa suggests, it seems the "time travel" on Game of Thrones is following the Novikov self-consistency principle, which means only one timeline exists and all events are fixed.
Similar time loops have been seen in movies and shows like Harry Potter and the Prisoner of Azkaban, 12 Monkeys, and Futurama.
In all of these, the characters discover through travelling back in time that they are simply enacting what has already happened.