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We present a numerical analysis of the average frequency dependence of a Jones matrix describing polarization-mode dispersion (PMD) with arbitrarily large differential group delay (DGD). Using a properly oriented autocorrelation matrix, we calculate the relative frequency dependence of the phase delays in the principal states of polarization (PSP) and of the cross coupling between the PSPs. Our results show that the averaged frequency dependence of these components scales with the product of the relative optical frequency times the average DGD. We also find a previously unknown correlation between the third-order PMD vector and the cross product of the first- and second-order PMD vector.