Aims. We investigate the composition of the noise in coordinate time series of several hundreds of extragalactic radio sources monitored by the geodetic VLBI program since 1979. The noise type is identified at all available timescales longer than one year, following the observational history of the source. Methods. We computed the Allan standard deviation of coordinate time series and developed a Monte Carlo test to evaluate the influence of the irregular sampling and error on data onto the

more »

... e type identification. We classified the radio sources into three categories depending on their type of noise and taking into account the dominating noise at different timescales: from the category AV0, which contains sources with a stable behavior at all timescales, to the category AV2, which contains sources whose coordinates are dominated by random walks at the longest timescales. Results. We found that almost no source exhibited "idealized" white noise. Only 5% of the 647 sources we studied belong to the category AV0 (stable sources). Moreover, we found that this class contains sources with relatively short observational histories, suggesting that after some years, a source whose astrometric position has shown a stable behavior is likely to become unstable. This questions the existence of the stable source paradigm and adds complementary information in the crucial task of selecting sources on which to base the axes of the celestial reference frame.