This study investigates the effect of stochastic model errors on the significance test for velocities in the analysis of a global positioning system (GPS) position time series. This effect is studied by considering the estimated probabilities of type I and type II errors occurring in the hypothesis testing. For this purpose, synthetic daily time series with 3-, 7-, and 10-year periods are considered. Many random samples are simulated for each series such that they include white noise (WN), flicker noise (FN), and random walk noise (RWN) with specified magnitudes. First, it is shown that an incorrect WN-only stochastic model almost always yields false-positive decisions in testing the velocities. Later on, noise magnitudes in the series are obtained through the least-squares variance components estimation (LS-VCE) method. Confidence interval estimates depict that the estimated velocity uncertainties may be biased because of estimation errors of variance components. However, the type I and type II error probabilities in testing the velocities do not change significantly for most of the series samples with WN and FN. For the time series consisting of WN, FN, and RWN, the error in estimating the RWN magnitude causes more effect on the uncertainty of velocity. In this case, type I error relating to the velocity estimation may, on average, be increased by 9.4% while type II error remains the same.