The analysis of pressure associated with the jet from a three-stream nozzle yields strong correlations between the near- and far-field. The pressure field is generated by LES, and far field pressure is calculated based on a Ffowcs-Williams-Hawking algorithm. For one combination of flow parameters (core premixed jet at M a = 1.6, tertiary wall jet at M a = 1, deck length L/Dh = 2), we document statistics of the pressure fluctuations in the near- and far-field. In various sections through the near field, regions of large fluctuations are identified as hot spots. The hot spot power spectra reveal some peaks of activity, notably around St = 0.2, visible in the side shear layers and in the first oblique compression shock in particular; and also broad-band activity centered in different frequency ranges. Most notably, the near field pressure exhibits some cyclic fluctuations, suggesting that the interactions between hot spots follow a repeated pattern. This is confirmed by phase averaging. The phase of a reference signal (pressure at a given hot spot) is determined from the phase angle of the complex Morlet wavelet coefficients, and the normalized Morlet coefficients at all points in the field are then averaged according to this reference phase. The resulting fluctuations show the propagation of fluctuations along shocks and mixing layers, around and across the jet. Furthermore, we find that the far-field also shows some phase-locking in this frquency range, particularly in the cone of coherent acoustic radiation surrounding the plume. We discuss the interest of phase-averaging in experiments where few sensor types can reach the required sampling rates.