More than two decades, continuous observations of permanent GPS stations used extensively for behavior of geodynamic phenomena have found such as deformation of the earth's crust, moving tectonic plates and fault. Daily position of permanent GPS stations are considered independent of each other in statistic. In other hand, some errors such as the satellite orbit modeling errors, determining parameters of rotation's earth, parameters of atmospheric modeling and etc; cause color noise or the correlation between daily positions of stations. Another important systematic error in GPS time series is offset. Offset by factors such as earthquakes, replace the GPS antenna, human and environmental errors are generated. Offset in GPS time series's functional model causes the bias estimation of unknown parameters Therefor, we require exact statistical model and function model of GPS time series to exact estimation of the speed parameter. For this purpose, multivariate noise analysis on 38 permanent GPS stations of Iran, were carried out by the period of 7 years (2006–2012), in this study. These stations are scattered throughout the country. In this analysis, statistical model of data presented of by incorporating white noise, flicker noise and random Walk noise and noise components estimation has taken place by  method of " least squares variance component estimation ". Also the effect of offset in the data were examined on estimation of noise and station's speed parameters by method of "least squares". The temporal correlation with multivariate noise analysis was performed for both single-station and multi- station. The results showed that noise amounts in coordinate series distributed due to processing all stations with each other in multi-station mode. In multivariate analysis single-station, Random Walk noise amounts after offset removal get zero in some stations, but in multi- station mode any stations were not zero for Random Walk noise. So single- station mode is more realistic than multi- station mode. Noises estimation from data with offset and compare them with results from data without offset shows offset effect on the amounts of noise, especially Random Walk noise that the greater part of it consist of offset. In addition to consideration of offset effect on noise, its effect on the speed parameters were also assessed. This assessment shows changes of length and direction of speed vector, after removing offset that examine necessity of offset's studying at data . So having the correct functional model and statistical model and without offset in the exact determination of parameters such as speed is essential. The studying of spatial correlation showed that there are significant correlation for components location North - North, East - East and height - height after removing offset, but correlation results are not significant between the various components of the coordinate, North - East, North - height and East - height. After removing offset of data, difference of speed vector from its average value, was calculated. It's found, speed of stations in tectonic boundaries (Saudi Arabia in the south and Eurasia tectonic plates in the north of Iran) more than center of Iran.