  Anyonic fractional charges $e^*$ have been detected by autocorrelation shot
noise at a quantum point contact (QPC) between two fractional quantum Hall
edges. We find that the autocorrelation noise can also show a fingerprint of
Abelian anyonic fractional statistics. We predict the noise of electrical
tunneling current $I$ at the QPC of the fractional-charge detection setup, when
anyons are dilutely injected, from an additional edge biased by a voltage, to
the setup in equilibrium. At large voltages, the nonequilibrium noise is {\it
reduced} below the thermal equilibrium noise by the value $2 e^* I$. This
negative excess noise is opposite to the positive excess noise $2e^* I$ of the
conventional fractional-charge detection and also to usual positive
autocorrelation noises of electrical currents. This is a signature of the
Abelian fractional statistics, resulting from the effective braiding of an
anyon thermally excited at the QPC around another anyon injected from the
additional edge.
