  We study the performance of the latest $H(z)$ data in constraining the
cosmological parameters of different cosmological models, including that of
Chevalier-Polarski-Linder $w_{0}w_{1}$ parametrization. First, we introduce a
statistical procedure in which the chi-square estimator is not affected by the
value of the Hubble constant. As a result, we find that the $H(z)$ data do not
rule out the possibility of either non-flat models or dynamical dark energy
cosmological models. However, we verify that the time varying equation of state
parameter $w(z)$ is not constrained by the current expansion data. Combining
the $H(z)$ and the Type Ia supernova data we find that the $H(z)$/SNIa overall
statistical analysis provides a substantial improvement of the cosmological
constraints with respect to those of the $H(z)$ analysis. Moreover, the
$w_{0}-w_{1}$ parameter space provided by the $H(z)$/SNIa joint analysis is in
a very good agreement with that of Planck 2015, which confirms that the present
analysis with the $H(z)$ and SNIa probes correctly reveals the expansion of the
Universe as found by the team of Planck. Finally, we generate sets of Monte
Carlo realizations in order to quantify the ability of the $H(z)$ data to
provide strong constraints on the dark energy model parameters. The Monte Carlo
approach shows significant improvement of the constraints, when increasing the
sample to 100 $H(z)$ measurements. Such a goal can be achieved in the future,
especially in the light of the next generation of surveys.
