  To obtain the most accurate pulse arrival times from radio pulsars, it is
necessary to correct or mitigate the effects of the propagation of radio waves
through the warm and ionised interstellar medium. We examine both the strength
of propagation effects associated with large-scale electron-density variations
and the methodology used to estimate infinite-frequency arrival times. Using
simulations of two-dimensional phase-varying screens, we assess the strength
and non-stationarity of timing perturbations associated with large-scale
density variations. We identify additional contributions to arrival times that
are stochastic in both radio frequency and time and therefore not amenable to
correction solely using times of arrival. We attribute this to the frequency
dependence of the trajectories of the propagating radio waves. We find that
this limits the efficacy of low-frequency (metre-wavelength) observations.
Incorporating low-frequency pulsar observations into precision timing campaigns
is increasingly problematic for pulsars with larger dispersion measures.
