  Let $\{X_n;n\ge 1\}$ be a sequence of independent and identically distributed
random variables on a sub-linear expectation space
$(\Omega,\mathscr{H},\widehat{\mathbb E})$, $S_n=X_1+\ldots+X_n$. We consider
the moments of $\max_{n\ge 1}|S_n|/\sqrt{2n\log\log n}$. The sufficient and
necessary conditions for the moments to be finite are given. As an application,
we obtain the law of the iterated logarithm for moving average processes of
independent and identically distributed random variables.
