  Using the simultaneous Infra-Red (IR) and X-ray light curves obtained by
Kalamkar et al. (2016), we perform a Fourier analysis of the IR/X-ray timing
correlations of the black hole X-ray binary (BHB) GX 339-4. The resulting IR vs
X-ray Fourier coherence and lag spectra are similar to those obtained in
previous studies of GX 339-4 using optical light curves. In particular, above 1
Hz, the lag spectrum features an approximately constant IR lag of about 100 ms.
We model simultaneously the radio to IR Spectral Energy Distribution (SED), the
IR Power Spectral Density (PSD), and the coherence and lag spectra using the
jet internal shock model ISHEM assuming that the fluctuations of the jet
Lorentz factor are driven by the accretion flow. It turns out that most of the
spectral and timing features, including the 100 ms lag, are remarkably well
reproduced by this model. The 100 ms time-scale is then associated with the
travel time from the accretion flow to the IR emitting zone. Our exploration of
the parameter space favours a jet which is at most mildly relativistic
($\bar{\Gamma}< 3$), and a linear and positive relation between the jet Lorentz
factor and X-ray light curve i.e. $\Gamma(t)-1\propto L_{X}(t)$. The presence
of a strong Low Frequency Quasi Periodic Oscillation (LFQPO) in the IR light
curve could be caused by jet precession driven by Lense-Thirring precession of
the jet-emitting accretion flow. Our simulations confirm that this mechanism
can produce an IR LFQPO similar to that observed in GX 339-4.
