When a time series shows no fixed mean and a specific seasonal pattern. The seasonality relevant to this type of time series might be modelled as both non-stationary and stationary components. The non-stationary part of seasonality is expressed by the seasonal integration factor, that is, $S(B)=1+B+B^2+\cdots+B^{p-1}$. The stationary part can be expressed by appropriate seasonal lag, that is, traditional Box-Jenkins SAR(p) model. For descripting the S(B) factor, there exist two explicit ways of modelling. The one is using S(B) itself and the other is the cyclical trend formulation. In this thesis, the latter model form is employed to modelling the diverging component of seasonality. The explicit decomposition of seasonality in stationary and non-stationary senses brings about more satisfactory result than not doing that in the context of the structural time series modelling.
