The past can...somewhat be changed. It can't be changed in the sense that, once you return to your original time, all of your memories of time-traveling will be erased. However, your heart will still follow any new motives gained, as if your memories weren't erased. Through that, history can be changed.
I think it always creates a stable time loop. Like, there was not a time where YMX in the past didn't have the urge to leave DI. however, this time travel aspect explains his heart's urge to leave.