  The twist of the magnetic field above a sunspot is an important quantity in
solar physics. For example, magnetic twist plays a role in the initiation of
flares and coronal mass ejections (CMEs). Various proxies for the twist above
the photosphere have been found using models of uniformly twisted flux tubes,
and are routinely computed from single photospheric vector magnetograms. One
class of proxies is based on $\alpha_z$, the ratio of the vertical current to
the vertical magnetic field. Another class of proxies is based on the so-called
twist density, $q$, which depends on the ratio of the azimuthal field to the
vertical field. However, the sensitivity of these proxies to temporal
fluctuations of the magnetic field has not yet been well characterized. We aim
to determine the sensitivity of twist proxies to temporal fluctuations in the
magnetic field as estimated from time-series of SDO/HMI vector magnetic field
maps. To this end, we introduce a model of a sunspot with a peak vertical field
of 2370 Gauss at the photosphere and a uniform twist density $q= -0.024$
Mm$^{-1}$. We add realizations of the temporal fluctuations of the magnetic
field that are consistent with SDO/HMI observations, including the spatial
correlations. Using a Monte-Carlo approach, we determine the robustness of the
different proxies to the temporal fluctuations. The temporal fluctuations of
the three components of the magnetic field are correlated for spatial
separations up to 1.4 Mm (more than expected from the point spread function
alone). The Monte-Carlo approach enables us to demonstrate that several proxies
for the twist of the magnetic field are not biased in each of the individual
magnetograms. The associated random errors on the proxies have standard
deviations in the range between $0.002$ and $0.006$ Mm$^{-1}$, which is smaller
by approximately one order of magnitude than the mean value of $q$.
