  The standard cosmographic approach consists in performing a series expansion
of a cosmological observable around $z=0$ and then using the data to constrain
the cosmographic (or kinematic) parameters at present time. Such a procedure
works well if applied to redshift ranges inside the $z$-series convergence
radius ($z<1$), but can be problematic if we want to cover redshift intervals
that fall outside the $z-$series convergence radius. This problem can be
circumvented if we work with the $y-$redshift, $y=z/(1+z)$, or the scale
factor, $a=1/(1+z)=1-y$, for example. In this paper, we use the scale factor
$a$ as the variable of expansion. We expand the luminosity distance and the
Hubble parameter around an arbitrary $\tilde{a}$ and use the Supernovae Ia (SNe
Ia) and the Hubble parameter data to estimate $H$, $q$, $j$ and $s$ at $z\ne0$
($\tilde{a}\neq1$). We show that the last relevant term for both expansions is
the third. Since the third order expansion of $d_L(z)$ has one parameter less
than the third order expansion of $H(z)$, we also consider, for completeness, a
fourth order expansion of $d_L(z)$. For the third order expansions, the results
obtained from both SNe Ia and $H(z)$ data are incompatible with the
$\Lambda$CDM model at $2\sigma$ confidence level, but also incompatible with
each other. When the fourth order expansion of $d_L(z)$ is taken into account,
the results obtained from SNe Ia data are compatible with the $\Lambda$CDM
model at $2\sigma$ confidence level, but still remains incompatible with
results obtained from $H(z)$ data. These conflicting results may indicate a
tension between the current SNe Ia and $H(z)$ data sets.
