If you possessed such a device then errors in your "predictions" would be indicative of another party using a similar device. As such, I assume multiple parties would soon discover each other, engage in an incomprehensibly complex time-battle, and there would suddenly (instantaneously in all patched timelines) be only one such party.

Furthermore, I imagine it would be very easy for such a party to accidently blunder into a situation where they lose control of the time-messaging device, erasing all evidence of its own existence and leaving the timeline perturbation-free until such "time" as reverse time travel is rediscovered.