This study focuses on the effects of time correlation in weekly GPS position time series on velocity estimates. Time series 2.5 to 13 years long from a homogeneously reprocessed solution of 275 globally distributed stations are analyzed in terms of noise content and velocity uncertainty assessment. Several noise models were tested, including power law and Gauss-Markov processes. The best noise model describing our global data set was a combination of variable white noise and power law noise models with mean amplitudes of ∼2 mm and ∼6 mm, respectively, for the sites considered. This noise model provided a mean vertical velocity uncertainty of ∼0.3 mm/yr, 4–5 times larger than the uncorrelated data assumption. We demonstrated that correlated noise content with homogeneously reprocessed data is dependent on time series length and, especially, on data time period. Time series of 2–3 years of the oldest data contain noise amplitude similar to that found for time series of 12 years. The data time period should be taken into account when estimating correlated noise content, when comparing different noise estimations, or when applying an external noise estimation to assess velocity uncertainty. We showed that the data period dependency cannot be explained by the increasing tracking network or the ambiguity fixation rate but is probably related to the amount and quality of recorded data.