  Recently, in \cite{GXHTM}, the authors established $L^p$-boundedness of
vector-valued $q$-variational inequalities for averaging operators which take
values in the Banach space satisfying martingale cotype $q$ property. In this
paper, we prove that martingale cotype $q$ property is also necessary for the
vector-valued $q$-variational inequalities, which is a question left open.
Moreover, we characterize UMD property and martingale cotype $q$ property in
terms of vector valued $q$-variational inequalities for Hilbert transform.
