  We investigate the time evolution of non-parametric morphological quantities
and their relationship to major mergers between $4\geq z \geq 2$ in
high-resolution cosmological zoom simulations of disk galaxies that implement
kinetic wind feedback, $H_2$-based star formation, and minimal ISM
pressurisation. We show that the resulting galaxies broadly match basic
observed physical properties of $z\sim 2$ objects. We measure the galaxies'
concentrations ($C$), asymmetries ($A$), and $Gini$ ($G$) and $M_{20}$
coefficients, and correlate these with major merger events identified from the
mass growth history. We find that high values of asymmetry provide the best
indicator for identifying major mergers of $>1:4$ mass ratio within our sample,
with $Gini$-$M_{20}\,$ merger classification only as effective for face-on
systems and much less effective for edge-on or randomly-oriented galaxies. The
canonical asymmetry cut of $A\geq0.35$, however, is only able to correctly
identify major mergers $\sim 10\%$ of the time, while a higher cut of $A\geq
0.8$ more efficiently picks out mergers at this epoch. We further examine the
temporal correlation between morphological statistics and mergers, and show
that for randomly-oriented galaxies, half the galaxies with $A\geq0.8$ undergo
a merger within $\pm0.2\,{\rm Gyr}$, whereas $Gini$-$M_{20}\,$ identification
only identifies about a third correctly. The fraction improves further using
$A\geq 1.5$, but about the half the mergers are missed by this stringent cut.
