Time series of position changes estimated from data from 236 continuously recording GPS receivers operating in Southern California and Southern Nevada are evaluated for noise models that characterize their temporal correlations. The lengths of the time series range between 3.5 and 10 years. After adjusting these data for postseismic deformation, offsets, and annual periodicities, I find that about one-half of the time series have temporal correlations that are categorized as either flicker or random-walk noise. The remaining time series can be best categorized as either a combination of flicker and random-walk; power law noise; first-order Gauss-Markov plus random-walk noise; or power law plus broadband, seasonal noise. A variety of geodetic monuments are used in Southern California and Nevada, including deeply braced designs, cement piers, pins drilled in outcrop, and buildings. When I evaluate the noise for each time series in terms of an estimate of the standard error in velocity, I find that the sites with the smallest errors are those located in Nevada using deeply braced monuments. Sites that are installed within regions of active pumping, both for groundwater and oil, had the largest standard errors in velocity. Comparison of monument stability, as measured by standard error in rate, with average, annual rainfall nearby indicates a marginally significant correlation. In addition, even though regional filtering removed much of the common-mode signals in these time series, there still remains a common-mode seasonal signal which can and should be removed.