The purpose of this thesis is to develop the new technique for the analysis of seasonal time series by extending the vector sample auto-correlation function(VSACF), which was developed for ARMA modelling procedure. After the problems of VSACF for modelling seasonal time series are investigated, the adjacent variance is defined and used for decomposing the seasonal factor from the seasonal time series. The seasonal indices are calculated and the VSACF is applied to the transformed series. The automatic procedure for modelling seasonal time series is suggested and applied to the real data, the international airline passenger travel.