The span of coordinate time series affects the determination of an optimal noise model. We analyzed position data recorded for 10 continuous Global Positioning System （GPS） sites from 1998.0 to mid-2009 on the Australian Plate to estimate the best noise model and thereafter obtain the true uncertainties of the velocity, employing the maximum likelihood estimation （MLE） method. MLE was employed to analyze the data in four ways. In the first two analyses, the noise was assumed to be a combination of flicker noise and white noise for the raw time series and spatially filtered time series. In the final two analyses, the spectral indices and amplitudes were simultaneously estimated for a power law noise plus white noise model for the raw time series and spatially filtered time series. We conclude that the noise model of GPS time series in Australia can be best described as the combination of flicker noise and white noise. Velocity uncertainties fall below -0.2 mm/yr when the time span exceeds -9.5 years. A comparison of noise amplitudes and maximum likelihood estimation values between the raw and spatially filtered time series suggests that traditional spatial filtering to remove common-mode errors might not be applicable to the raw time series of this region.
