  The active galactic nucleus (AGN) RE J1034+396 displays the most significant
X-ray Quasi-Periodic Oscillation (QPO) detected so far. We perform a detailed
spectral-timing analysis of our recent simultaneous XMM-Newton, NuSTAR and
Swift observations. We present the energy dependence of the QPO's frequency,
rms, coherence and phase lag, and model them together with the time-averaged
spectra. Our study shows that four components are required to fit all the
spectra. These components include an inner disc component (diskbb), two warm
corona components (CompTT-1 and CompTT-2), and a hot corona component
(nthComp). We find that diskbb, CompTT-2 (the hotter but less luminous
component) and nthComp all contain the QPO signal, while CompTT-1 only exhibits
stochastic variability. By fitting the lag spectrum, we find that the QPO in
diskbb leads CompTT-2 by 679 s, and CompTT-2 leads nthComp by 180 s. By only
varying the normalizations, these components can also produce good fits to the
time-averaged and variability spectra obtained from previous observations when
QPOs were present and absent. Our multi-wavelength study shows that the
detectability of the QPO does not depend on the contemporaneous mass accretion
rate. We do not detect a significant Iron K{\alpha} emission line, or any
significant reflection hump. Finally, we show that the rms and lag spectra in
the latest observation are very similar to the 67 Hz QPO observed in the
micro-quasar GRS 1915+105. These new results support the physical analogy
between these two sources. We speculate that the QPO in both sources is due to
the expansion/contraction of the vertical structure in the inner disc.
