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We apply a series of null diagnostics based on the statefinder hierarchy todiagnose different holographic dark energy models including the originalholographic dark energy, the new holographic dark energy, the new agegraphicdark energy, and the Ricci dark energy models. We plot the curves ofstatefinders $S^{(1)}_3$ and $S^{(1)}_4$ versus redshift $z$ and theevolutionary trajectories of $\{S^{(1)}_3, \epsilon\}$ and $\{S^{(1)}_4,\epsilon\}$ for these models, where $\epsilon$ is the fractional growthparameter. Combining the evolution curves with the current values of$S^{(1)}_3$, $S^{(1)}_4$, and $\epsilon$, we find that the statefinder$S^{(1)}_4$ performs better than $S^{(1)}_3$ for diagnosing the holographicdark energy models. In addition, the conjunction of the statefinder hierarchyand the fractional growth parameter is proven to be a useful method to diagnosethe holographic dark energy models, especially for breaking the degeneracy ofthe new agegraphic dark energy model with different parameter values.

Diagnosing holographic dark energy models with statefinder hierarchy