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Common Mode Error (CME) means the sum of environmental and technique-dependent systematic errors in GPS position time series. The CME, which is a kind of the temporally correlated noise, can be seen in the time series from regional GNSS networks that spans hundreds of kilometers. This paper concerns the results of studies regarding the necessity of spatio-temporal filtration of time series to determine highly reliable velocities of permanent stations for the geophysical (plate motion or earthquakes) studies or to maintain the kinematic reference frames. In this research the JPL (Jet Propulsion Laboratory) PPP solution processed by GIPSY-OASIS software were taken. Trend and seasonal signals were removed using least-squares estimation to form the residual time series. Then, the internal structure (CME) of the set of residual time series with orthogonal transformations was revealed. We examined the Principal Component Analysis (PCA) and assumed the existence of a non-uniform spatial response in the network to the CME. We confirmed our theoretical assumptions about the benefits of the PCA approach when stations in a network are potentially affected by local effects. We noticed for height time series, that noise amplitudes decreased from 0.5 to 13.5 mm/year(-kappa/4) after filtration. That gave a relative reduction of amplitudes ranging between 4 % and 76 % for all stations, while the average improvement was 49 %. The average relative increase of spectral index was equal to 48 %. One of the most important consequences related to spatio-temporal GNSS time series filtering is improvement (better credibility) of accuracy of the determined velocity. The accuracy of velocity, after filtration, was lower for Up component of all stations. The average reduction was 0.2 mm/year, while maximal reached 0.8 mm/year. Above described result mean that the reduction of accuracy relative to the after-filtration accuracy was on average about 70 %.