  We study why the calculation of current correlation functions (CCFs) still
suffers from finite size effects even when the periodic boundary condition is
taken. Two important one dimensional, momentum conserving systems are
investigated as examples. Intriguingly, it is found that the state of a system
recurs in the sense of microcanonical ensemble average, and such recurrence may
result in oscillations in CCFs. Meanwhile, we find that the sound mode
collisions induce an extra time decay in a current so that its correlation
function decays faster (slower) in a smaller (larger) system. Based on these
two unveiled mechanisms, a procedure for correctly evaluating the decay rate of
a CCF is proposed, with which our analysis suggests that the global energy CCF
decays as $\sim t^{-\frac{2}{3}}$ in the diatomic hard-core gas model and in a
manner close to $\sim t^{-\frac{1}{2}}$ in the Fermi-Pasta-Ulam-$\beta$ model.
