The time series of 72 international GPS service core stations were selected to make perform analysis on GPS noise model and uncertainties of the velocity. An improved Akaike information criteria and a Bayesian information criteria model were developed to evaluate different combinations of noise model, so as to establish the best noise model of GPS time series and gain the aureate velocity parameters. Results show that the noise model of GPS time series cannot be described as simple noise, it tends to showing diversity, and can be best described by power-law, generalized Gauss Markov, flicker noise plus white noise model, and its three components exhibit different noise characteristics. With the time span increases, the optimal noise model of time series, GPS station velocity and its uncertainty tends to be convergent and steady. Besides, the proportion of random walk noise is proved to increase as time span increases. The final results show that the time span of more than 10 years is an ideal noise model estimation scale.