I choose to believe in the split timeline theory, myself.

Every action you do creates a seperate timeline.

Each timeline then branches off into more timelines and so on and so forth.

But travelling back in time won't change the future, but rather create an infinite number of timelines- one from deciding if you want to go to the path, and then the others deciding which year. The same thing happens when you try to kill yourself. One to decide if you do it or not, the rest to decide the time, place, and death method 

But if you believe that time is just a circle of fragile string, then going back in time to kill yourself will just cut the future of the string from that moment and tie a new string together from there. You would cease to exist, but then you would exist again to either repeat that mistake, or to forget it ever happened.