We estimated the common seasonal signal (annual oscillation) included in the Global Positioning System (GPS) vertical position time series by using Multichannel Singular Spectrum Analysis (MSSA). We employed time series from 24 International GNSS Service (IGS) stations located in Europe which contributed to the newest ITRF2014 (International Terrestrial Reference Frame). The MSSA method has an advantage over the traditional modelling of seasonal signals by the Least-Squares Estimation (LSE) and Singular Spectrum Analysis (SSA) approaches because it can extract time-varying and common seasonal oscillations for stations located in the considered area. Having estimated the annual curve with LSE, we may make a misfit of 3 mm when a peak-to-peak variations of seasonal signals are to be estimated due to the time-variability of seasonal signal. A variance of data modelled as annual signal with SSA and MSSA differs of 3 % at average what proves that the MSSA-curves contain only time-varying and common seasonal signal and leave the station-specific part, local phenomena and power-law noise intact. In contrast to MSSA, these effects are modelled by SSA. The differences in spectral indices of power-law noise between MSSA and LSE estimated with Maximum Likelihood Estimation (MLE) are closer to zero than the ones between SSA and LSE, which means that MSSA curves do not contain site-specific noise as much as the SSA curves do.