  A word $w$ is said to be closed if it has a proper factor $x$ which occurs
exactly twice in $w$, as a prefix and as a suffix of $w$. Based on the concept
of Ziv-Lempel factorization, we define the closed $z$-factorization of finite
and infinite words. Then we find the closed $z$-factorization of the infinite
$m$-bonacci words for all $m \geq 2$. We also classify closed prefixes of the
infinite $m$-bonacci words.
