We consider holographic cosmological models of dark energy in which the infrared cutoff is set by the Hubbles 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.
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