Cosmographic approach to Running Vacuum dark energy models: new
  constraints using BAOs and Hubble diagrams at higher redshifts
  In this work we study different types of dark energy (DE) models in the
framework of the cosmographic approach, with emphasis on the Running Vacuum
models (RVMs). We assess their viability using different information criteria
and compare them with the so-called Ghost DE models (GDEs) as well as with the
concordance $\Lambda$CDM model. We use the Hubble diagrams for Pantheon SnIa,
quasars (QSOs), gamma-ray bursts (GRBs) as well as the data on baryonic
acoustic oscillations (BAOs) in four different combinations. Upon minimizing
the $\chi^2$ function of the distance modulus in the context of the Markov
Chain Monte Carlo method (MCMC), we put constraints on the current values of
the standard cosmographic parameters in a model-independent way. It turns out
that, in the absence of BAOs data, the various DE models generally exhibit
cosmographic tensions with the observations at the highest redshifts (namely
with the QSOs and GRBs data). However, if we include the robust observations
from BAOs to our cosmographic sample, the $\Lambda$CDM and RVMs are clearly
favored against the GDEs. Finally, judging from the perspective of the deviance
information criterion (DIC), which enables us to compare models making use of
the Markov chains of the MCMC method, we conclude that the RVMs are the
preferred kind of DE models. We find it remarkable that these models, which had
been previously shown to be capable of alleviating the $\sigma_8$ and $H_0$
tensions, appear now also as the most successful ones at the level of the
cosmographic analysis.
