  Context: Solar eruptions, such as coronal mass ejections (CMEs), are often
accompanied by accelerated electrons that can in turn emit radiation at radio
wavelengths. This radiation is observed as solar radio bursts. The main types
of bursts associated with CMEs are type II and type IV bursts that can
sometimes show movement in the direction of the CME expansion, either radially
or laterally. However, the propagation of radio bursts with respect to CMEs has
only been studied for individual events. Aims: Here, we perform a statistical
study of 64 moving bursts with the aim to determine how often CMEs are
accompanied by moving radio bursts. This is done in order to ascertain the
usefulness of using radio images in estimating the early CME expansion.
Methods: Using radio imaging from the Na\c{c}ay Radioheliograph (NRH), we
constructed a list of moving radio bursts, defined as bursts that move across
the plane of sky at a single frequency. We define their association with CMEs
and the properties of associated CMEs using white-light coronagraph
observations. We also determine their connection to classical type II and type
IV radio burst categorisation. Results: We find that just over a quarter of
type II and half of type IV bursts that occurred during the NRH observing
windows in Solar Cycle 24 are accompanied by moving radio emission. All but one
of the moving radio bursts are associated with white--light CMEs and the
majority of moving bursts (90%) are associated with wide CMEs (>60 degrees in
width). In particular, all but one of the moving bursts corresponding to type
IIs are associated with wide CMEs; however, and unexpectedly, the majority of
type II moving bursts are associated with slow white-light CMEs (<500 km/s). On
the other hand, the majority of moving type IV bursts are associated with fast
CMEs (>500 km/s).
