This is essentially a variation of the grandfather paradox, in which you do events that causes your existence to fade away. If you kill yourself, one of these scenarios might happen.

The Boring Theory

MULTIVERSE! This creates another universe in which you from the future murders you from the past. The universe remains intact and all is well, but with changes in the future due to your presence not being felt in the future.

The Theory that Loves You

In this theory, the universe itself would prevent you from ever reaching your past self, thus unable to kill your past self. Call it fate intervening.