  We propose a new parametrization of the deceleration parameter to study its
time-variation behavior. The advantage of parameterizing the deceleration
parameter is that we do not need to assume any underlying theory of gravity. By
fitting the model to the 157 gold sample supernova Ia data, we find strong
evidence that the Universe is currently accelerating and it accelerated in the
past. By fitting the model to the 115 nearby and Supernova Legacy Survey
supernova Ia data, the evidence that the Universe is currently accelerating is
weak, although there is still a strong evidence that the Universe once
accelerated in the past. The results obtained from the 157 gold sample
supernova Ia data and those from the 115 supernova Ia data are not directly
comparable because the two different data sets measure the luminosity distance
up to different redshifts.
  We then use the Friedmann equation and a dark energy parametrization to
discuss the same problem. When we fit the model to the supernova Ia data alone,
we find weak evidence that the Universe is accelerating and the current matter
density is higher than that measured from other experiments. After we add the
Sloan Digital Sky Survey data to constrain the dark energy model, we find that
the behavior of the deceleration parameter is almost the same as that obtained
from parameterizing the deceleration parameter.
