When a fiber is characterized by measured polarization mode dispersion (PMD) vector data, inversion of these data is required to determine the frequency dependence of the fiber's Jones matrix and, thereby, its pulse response. We briefly review approaches to PMD inversion and discuss three second-order models used for this purpose. We report extension of inversion to fourth-order PMD using higher-order concatenation rules, rotations of higher power designating higher rates of acceleration with frequency, and representation of these rotations by Stokes vectors.