Standard time series analysis techniques have been applied to the homogeneous polar motion data recently published by the ILS--IPMS in order to study some of the more controversial features apparently possessed by the older ILS data. The magnitude and direction of the secular trend unbiased by the presence of harmonics in the data were determined, yielding a rate of polar wander ~3.52¿10-3 arc sec/yr (which extrapolates to ~0.98¿/m.y.) in direction 80.1 ¿W longitude. The long-period Markowitz wobble, which dominates the retrograde power spectrum of data, has a signal to noise ratio in that spectrum of 21:1; its period is well-determined as 31 years. Variations with time of the annual wobble and Chandler wobble were investigated using complex demodulation; the annual wobble was found to undergo relatively insignificant variations in amplitude and phase, in contrast to some analyses of the older ILS data, while the amplitude modulation and 1925--1940 phase change of the Chandler wobble were reconfirmed.