  The dynamics of systems subjected to noise is called Markovian in the absence
of memory effects, i.e. when its immediate future only depends on its present.
Time correlations in the noise source may generate non-Markovian effects that,
sometimes, can be erased by appropriately coarse graining the time evolution of
the system. In general, the coarse graining time $t_\text{CG}$ is taken to be
much larger than the correlation time $\tau$ but no direct relation between
them is established. Here we analytically obtain a relation between
$t_\text{CG}$ and $\tau$ for the dynamics of a qubit subjected to a time
correlated environment. Our results can be applied in principle to any
distribution of the environmental correlations and can be tested through a
collisional model where the qubit sequentially interacts with correlated
qutrits.
