Continuous GPS (CGPS) coordinate time-series are known to experience repeating deformation signals with seasonal and other periods. It is unlikely that these signals represent perfect sinusoids with temporally constant amplitude. We develop an analysis method that accommodates temporal variations in the amplitudes of sinusoidal signals. We apply the method to simulated coordinate time-series to numerically explore the potential consequences of neglecting decadal variation in amplitude of annual motions on the residual-error spectra of CGPS measurements, as well as potential bias in estimates for secular site velocity. We find that secular velocity bias can be appreciable for shorter time-series, and that residual-error time-series of longer duration may contain significant power in a broad band centred on semi-annual frequency if temporal variation in the amplitude of annual motions is not accounted for in the model used to reduce the observations to residuals. It may be difficult to differentiate the bandpass filtered signature of mismodelled loading signals from power-law noise, using residual-error spectra for shorter time-series. We provide an example application to a ∼9-yr coordinate time-series for a CGPS station located in southern California at Carbon Creek Control Structure (CCCS), which is known to experience large amplitude seasonal motions associated with the Santa Ana aquifer system.