  We consider holographic cosmological models of dark energy in which the
infrared cutoff is set by the Hubble's radius. We show that any interacting
dark energy model with a matter like term able to alleviate the coincidence
problem (i.e., with a positive interaction term, regardless of its detailed
form) can be recast as a noninteracting model in which the holographic
parameter evolves slowly with time. Two specific cases are analyzed. First, the
interacting model presented in [1] is considered, and its corresponding
noninteracting version found. Then, a new noninteracting model, with a specific
expression of the time-dependent holographic parameter, is proposed and
analyzed along with its corresponding interacting version. We constrain the
parameters of both models using observational data, and show that they can be
told apart at the perturbative level.
