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Recent direct $H(z)$ data indicate that the parameter $H(z)$ may wiggle withrespect to $z$. On the other hand the luminosity distance data of supernovaeflatten the wiggles of $H(z)$ because of integration effect. It is expectedthat the fitting results can be very different in a model permitting a wiggling$H(z)$ because the data of supernovae is highly degenerated to such a model. Asan example the natural phantom dark energy is investigated in this paper. Thedynamical property of this model is studied. The model is fitted by the direct$H(z)$ data set and the SNLS data set, respectively. And the results are quitedifferent, as expected. The quantum stability of this model is also shortlydiscussed. We find it is a viable model if we treat it as an effective theorytruncated by an upperbound.Comment: 14 pages, 2 figures, discussions on the stability added, conclusions  not change

Natural phantom dark energy, wiggling Hubble parameterH(z) and directH(z) data