A total of 954 continuous GPS position time series from 414 individual sites in nine different GPS solutions were analyzed for noise content using maximum likelihood estimation (MLE). The lengths of the series varied from around 16 months to over 10 years. MLE was used to analyze the data in two ways. In the first analysis the noise was assumed to be white noise only, a combination of white noise plus flicker noise, or a combination of white noise plus random walk noise. For the second analysis the spectral index and amplitude of the power law noise were estimated simultaneously with the white noise. In solutions where the sites were globally distributed, the noise can be best described by a combination of white noise plus flicker noise. Both noise components show latitude dependence in their amplitudes (higher at equatorial sites) together with a bias to larger values in the Southern Hemisphere. In the regional solutions, where a spatially correlated (common mode) signal has been removed, the noise is significantly lower. The spectral index of the power law in regional solutions is more varied than in the global solutions and probably reflects a mixture of local effects. A significant reduction in noise can be seen since the first continuous GPS networks began recording in the early 1990s. A comparison of the noise amplitudes to the different monument types in the Southern California Integrated GPS Network suggests that the deep drill braced monument is preferred for maximum stability.