  The Madden-Julian Oscillation (MJO) has been studied using its daily RMM1,
RMM2 and VPM1, VPM2 principal components' indices. A spectral analysis of the
raw indices indicates presence of a noise presumably contributed by the random
high-frequency waves. A soft simple filter - 3 day running average, has been
applied to filter out this high-frequency noise (the filter has been chosen in
accordance with the observationally known properties of these waves). Power
spectrum of the smoothed indices exhibits a stretched exponential decay $E(f)
\propto \exp-(f/f_0)^{1/2}$ characteristic to the Hamiltonian distributed chaos
with spontaneously broken time translational symmetry (with time depending
Hamiltonian and adiabatic invariance of the action). An impact of the MJO's
Hamiltonian distributed chaos on the Asian-Australian Monsoons at the
intraseasonal time scales has been briefly discussed.
