  We introduce an estimation method for the scaled skewness coefficient of the
sample mean of short and long memory linear processes. This method can be
extended to estimate higher moments such as curtosis coefficient of the sample
mean. Also a general result on computing all asymptotic moments of partial sums
is obtained, allowing in particular a much easier derivation of some existing
central limit theorems for linear processes. The introduced skewness estimator
provides a tool to empirically examine the error of the central limit theorem
for long and short memory linear processes. We also show that, for both short
and long memory linear processes, the skewness coefficient of the sample mean
converges to zero at the same rate as in the i.i.d. case.
