  The higher twist contributions to the deeply inelastic structure functions
$F_2^{p}(x,Q^2)$ and $F_2^{d}(x,Q^2)$ for larger values of the Bjorken variable
$x$ are extracted extrapolating the {twist--2} contributions measured in the
large $W^2$ region to the region $4 \GeV^2 \leq W^2 \leq 12.5 \GeV^2$ applying
target mass corrections. We compare the results for the NLO, NNLO and N$^3$LO
analyzes and include also the large $x$ at N$^4$LO to the Wilson coefficients.
A gradual lowering of the higher twist contributions going from NLO to N$^4$LO
is observed, which stresses the importance of higher order corrections.
