The qualification and the maintenance of the International Celestial Reference Frame (ICRF) source directions are currently based on global statistics regarding the complete data set of VLBI observations of extragalactic radio sources. The founding hypothesis in the selection of extragalactic objects to access a quasi-inertial reference system is that their directions are fixed in space. Therefore the study of the time variability of the sources is an important step in the process of checking and improving the reliability of the ICRF, in view of high precision applications such as Earth rotation studies or the unification with future space astrometry results. In this paper we investigate the systematic and random behaviours in time seri...