In September 1991, the U. S. Geological Survey began continuous operation of two permanent Global Positioning System (GPS) sites near the Hayward fault. We use two and one half years of data from an 8‐km baseline to investigate GPS processing strategies, errors in the time and frequency domains, and the uncertainties of rates of change calculated from such data. Experiments with session lengths show that at least 6 hours of data should be used to obtain a precision of 2 to 4 mm. Experiments with broadcast and improved orbits show that the broadcast orbit is sufficient for this short baseline. Single‐frequency solutions have larger rms scatter; for scenarios made mostly in daylight, ionospheric delay systematically shortens the baseline length by 2.4 parts per million for L1 and 4.0 parts per million for L2. For the dual‐frequency results, the rms scatter about the best‐fitting straight line is 2.1 mm for baseline length, 2.2 mm for north, 2.9 mm for east, and 11.2 mm for vertical. For Winton relative to Chabot, the rates of change are −0.6±0.1 mm/yr in length, 2.8±0.1 mm/yr in north, −8.1±0.2 mm/yr in east, and −8.1±0.6 mm/yr in vertical. The baseline rate of change is consistent with right‐lateral shear across the Hayward fault but is not consistent with the −3.5 mm/yr predicted by the model of Lienkaemper et al. (1991). The large westward and downward motion of Winton relative to Chabot may be due to monument instability. Power spectra appear white at high frequencies; the estimated standard deviations for periods shorter than 5 days are 1.2 mm for length and north, 1.9 mm for east, and 5.5 mm for vertical. Power spectral density increases only slightly as frequency decreases from 0.2 to 0.03 cycle per day, and there is no distinct corner. In particular, no characteristic 1/ƒ2 signature of random walk monument noise emerges from the white noise. Estimated autocorrelations for length, north, east, and vertical fall to about 0.1 for lag times shorter than 10 days and fluctuate about zero for lag times longer than about 25 days. Because the time series is short, it is possible that random walk monument noise exists but is undetectable in the estimated power spectral density and autocorrelation functions. We use the estimated full covariance matrix to calculate the standard deviations of the baseline rate of change for various sampling schemes. The theoretical standard deviation of dL/dt determined from 1 year of daily observations is 0.28 times that determined from 1 year of annual observations. We can obtain a similar uncertainty from 2 years of measurements made every 30 days and better results from 5 years of annual measurements. However, daily measurements allow the detection and correction of offsets that sometimes occur with equipment or firmware changes.