GPS height time series used in geophysical studies are often formed from discrete, continuous, nonoverlapping 24 hour processing sessions. With such a strategy, unmodeled periodic ground displacements with approximately semidiurnal and diurnal periods have often been assumed to average close to zero. By analyzing several years of continuous GPS data from globally distributed sites at which controlled errors were not modeled, this paper shows such an assumption to be erroneous. It is shown that each unmodeled (sub-) daily periodic displacement can propagate to several spurious long-wavelength features in a GPS height time series, ranging in period from about 2 weeks to 1 year. Admittances (ratio of amplitude of spurious long-wavelength output signal in the GPS height time series to amplitude of unmodeled periodic ground displacement) depend on the coordinate component and the tidal constituent considered. For example, it is shown that an unmodeled S2 north component periodic ground displacement can propagate to a semiannual height signal with admittance of greater than 100%, whereas the height admittance is around 5--10%. Since model errors in ocean tide loading, atmospheric pressure loading, and solid earth tide displacement amplitudes can be several millimeters, long-wavelength spurious signals of up to these amplitudes may be expected to appear in GPS height time series. This paper provides an indication of how such errors will propagate, where such errors are greatest and hence how spurious fortnightly, semiannual, and, in some cases, annual effects may be present at some sites.