GX 339–4 is a black hole X-ray binary that is a key focus of accretion studies, since it goes into outburst roughly every 2–3 yr. Tracking of its radio, infrared (IR), and X-ray flux during multiple outbursts reveals tight broad-band correlations. The radio emission originates in a compact, self-absorbed jet; however, the origin of the X-ray emission is still debated: jet base or corona? We fit 20 quasi-simultaneous radio, IR, optical, and X-ray observations of GX 339–4 covering three separate outbursts in 2005, 2007, 2010–2011, with a composite corona+jet model, where inverse Compton emission from both regions contributes to the X-ray emission. Using a recently proposed identifier of the X-ray variability properties known as power-spectral hue, we attempt to explain both the spectral and evolving timing characteristics, with the model. We find the X-ray spectra are best fit by inverse Compton scattering in a dominant hot corona (kT_e ∼ hundreds of keV). However, radio and IR-optical constraints imply a non-negligible contribution from inverse Compton scattering off hotter electrons (kT_e ≥ 511 keV) in the base of the jets, ranging from a few up to ∼50 per cent of the integrated 3–100 keV flux. We also find that the physical properties of the jet show interesting correlations with the shape of the broad-band X-ray variability of the source, posing intriguing suggestions for the connection between the jet and corona
