  The non-Hermitian but $\mathcal{PT}$-symmetric quantum field theories are
known to have a pseudo-Hermitian interpretation. However the corresponding
intertwining operator happens to be nonlocal that raises the question to what
extent this nonlocality affects observable quantities. We consider the case
when the intrinsic parity of the interaction terms is determined by degree of
coupling constant. We show that the perturbative S-matrix of the equivalent
Hermitian description can be easily obtained from the perturbative S-matrix of
the non-Hermitian model. Namely, the first order vanishes whereas the second
order is given by the real part of the second order T-matrix of the
non-Hermitian model. We compute directly the 2-point and 4-point correlation
functions in the equivalent Hermitian model for the $i\phi^3$ model and find
the results consistent with this relation. The 1-loop correction to the mass
happens to be real reflecting the disappearance of 2-body decays. However the 2
to 2 scattering amplitude obtained using LSZ formula has poles taken in
principal value which implies the violation of the causality.
