Observational constraints and diagnostics for time-dependent dark energy
  models
  In this paper, we constrain four time-dependent dark energy (TDDE) models by
using the Type Ia supernovae (SNe Ia), baryonic acoustic oscillations (BAO),
observational Hubble parameter (OHD) data-sets as well as the single data point
from the newest event GW150914. Subsequently, adopting the best fitting values
of the model parameters, we apply the original statefinder, statefinder
hierarchy, the growth rate of matter perturbations and $Om(z)$ diagnostics to
distinguish the TDDE scenarios and the $\Lambda$CDM scenario from each other.
We discover that all the TDDE models and $\Lambda$CDM model can be
distinguished better at the present epoch by using the statefinder hierarchy
than using the original statefinder, the growth rate of matter perturbations
and $Om(z)$ diagnostics, especially, in the planes of
$\{S_3^{(1)},S_4^{(1)}\}$, $\{S_3^{(2)},S_4^{(2)}\}$, $\{S_5^{(1)},S_5^{(2)}\}$
and $\{S_4^{(2)},S_5^{(2)}\}$.
