To calculate the parton distribution functions (PDF) from first principles using lattice gauge theories
it is convenient to consider the Ioffe-time distribution defined through gauge-invariant bi-local operators with spacelike separation.
Lattice calculations provide values for a limited range of the distance separating the bi-local operators.
In order to perform the Fourier transform and obtain the pseudo- and the quasi-PDFs, it is then necessary
to extrapolate the large-distance behavior.

I will discuss the formalism one may use to study the behavior of
the Ioffe-time distribution at large distances
and show that the pseudo-PDF and quasi-PDF are very different in this regime.
Using light-ray operators, I will also show
that the higher twist corrections of the quasi-PDF come in not as inverse powers of $P$ but
as inverse powers of $x_B P$.