We analyze time series of daily positions estimated from data collected by 10 continuously monitoring Global Positioning System (GPS) sites in southern California during the 19-month period between the June 28, 1992 (MW=7.3), Landers and January 17, 1994 (MW=6.7), Northridge earthquakes. Each time series exhibits a linear tectonic signal and significant colored noise. Spectral power at frequencies in the range 5 yr-1 to 0.5 d-1 is dominated by white noise or possibly fractal white noise and is several orders of magnitude higher than what would be expected from random walk noise (in this short-period range) attributed by others to geodetic monument motions. Estimating a single slope for the time series' power spectra suggests fractal white noise processes with spectral indices of about 0.4. Site velocity uncertainties assuming this fractal white noise model are 2--4 times larger than uncertainties obtained assuming a purely white noise model. A combination white noise plus flicker noise (spectral index of 1) model also fits the data and suggests that the velocity uncertainties should be 3--6 times larger than for the white noise model. We cannot adequately distinguish between these two noise models, nor can we rule out the possibility of a random walk signal at the lowest frequencies; these questions await the analysis of longer time series. In any case, reducing the magnitude of low-frequency colored noise is critical and appears to be best accomplished by building sites with deeply anchored and braced monuments. Otherwise, rate uncertainties estimated from continuous GPS measurements may not be improved significantly compared to those estimated from infrequent campaign-mode measurements.¿ 1997 American Geophysical Union