  It has been alleged in several papers that the so called delayed
continuous-time random walks (DCTRWs) provide a model for the one-dimensional
telegraph equation at microscopic level. This conclusion, being widespread now,
is strange, since the telegraph equation describes phenomena with finite
propagation speed, while the velocity of the motion of particles in the DCTRWs
is infinite. In this paper we investigate how accurate are the approximations
to the DCTRWs provided by the telegraph equation. We show that the diffusion
equation, being the correct limit of the DCTRWs, gives better approximations in
$L_2$ norm to the DCTRWs than the telegraph equation. We conclude therefore
that, first, the DCTRWs do not provide any correct microscopic interpretation
of the one-dimensional telegraph equation, and second, the kinetic (exact)
model of the telegraph equation is different from the model based on the
DCTRWs.
