Most GPS time-series exhibit a seasonal signal that can have an amplitude of a few millimetres. This seasonal signal can be removed by fitting an extra sinusoidal signal with a period of one year to the GPS data during the estimation of the linear trend.However. Blewitt and Lavallee (2002) showed that including an annual signal in the estimation process still can give a larger linear trend error than the trend error estimated from data from which the annual signal has been removed by other means. They assumed that the GPS data only contained white noise and we extend their result to the case of power-law plus white noise which is known to exist in most GPS observations. For the GPS stations CASC, LAGO, PDEL and TETN the difference in trend error between having or not having an annual signal in the data is around ten times larger when a power-law plus white noise model is used instead of a pure white noise model. Next, our methodology can be used to estimate for any station how much the accuracy of the linear trend will improve when one tries to subtract the annual signal from the GPS time-series by using a physical model.Finally, we demonstrate that for short time-series the trend error is more influenced by the fact that the noise properties also need to be estimated from the data. This causes on average an underestimation of the trend error. (C) 2009 Elsevier Ltd. All rights reserved.