Turbulent flows in minimal flow units (MFUs) provide intrinsic information on near-wall physics of turbulence and help to develop useful models for numerical simulations. In the present study, MFUs at friction Reynolds numbers ranging from 1000 to 4000 are simulated. The space–time spectra and correlations of velocity and pressure fluctuations are computed. Two models, i.e., the elliptic approximation and the local amplitude modulated wave method are tested against the MFU data, and their performances in representing and reconstructing space–time spectra and correlations are evaluated. The models are then utilized to analyze the space–time characteristics of MFUs. An important feature of MFUs – the Reynolds number independence – holds for space–time statistics as well as the energy spectra. Comparisons are further carried out among the space–time statistics of velocity components and pressure, at different heights and scales. It is shown that despite the anisotropy in space, the space–time distributions of the three components of velocity fluctuations are quite similar. The scale dependence of convection speed is weak even near the wall, but that of sweeping velocity is always strong. The spanwise-temporal spectra and correlations are also presented, of which the proper modeling requires future work.