In this article, a new way to characterize the percolation threshold of polymer nanocomposites made of polyethylene (PE) with single and multi walled carbon nanotubes (SWCNTs and MWCNTs) is presented. Small and large oscillatory shear (SAOS and LAOS) experiments were performed to characterize the degree of dispersion and percolation threshold. The analysis of the stress response in the LAOS regime as a function of the applied deformation amplitude and frequency was performed using Fourier Transform (FT)-Rheology. The zero strain intrinsic nonlinear parameter, $Q_0({omega})$, was calculated by extrapolation of $I_{3/1}({gamma}_0,{omega})$ and was, used to quantify the nonlinearity measured by FT-Rheology. Interestingly, a drop in $Q_0$ as a function of the CNT weight fraction at a fixed frequency was found that was below the percolation threshold. This was followed by, a steep rise in $Q_0$ above the percolation threshold. Therefore, the new method based on this observation that is proposed and described with this article has the potential to lead to a better understanding of structure-property relationships in polymer nanocomposites.