Luminescence spectra of V-groove GaAs/AlGaAs quantum wires are investigated by spatially resolved photoluminescence (PL) spectroscopy using a low temperature scanning near-field optical microscope (SNOM). The statistical analysis of these spectra in terms of the autocorrelation function reveals the presence of level repulsion. We find that the comparison between the experimental autocorrelation curve and the theoretical one obtained from the simulation of PL spectra, assuming for each exciton state a Lorentzian lineshape, is unsatisfactory. This is due to the presence of a broad background in the measured spectra, which is absent in the simulated ones. We propose an improvement of the theoretical model in order to include this feature and propose as explanation for the origin of this broad background the coupling between a single exciton state and the phonon thermal bath. The addition of this last element in our model is very important to establish a better quantitative agreement between the simulated and measured autocorrelation functions.