  The autoregressive moving average (ARMA) model takes the significant position
in time series analysis for a wide-sense stationary time series. The difference
operator and seasonal difference operator, which are bases of ARIMA and SARIMA
(Seasonal ARIMA), respectively, were introduced to remove the trend and
seasonal component so that the original non-stationary time series could be
transformed into a wide-sense stationary one, which could then be handled by
Box-Jenkins methodology. However, such difference operators are more practical
experiences than exact theories by now. In this paper, we investigate the power
of the (resp. seasonal) difference operator from the perspective of spectral
analysis, linear system theory and digital filtering, and point out the
characteristics and limitations of (resp. seasonal) difference operator.
Besides, the general method that transforms a non-stationary (the
non-stationarity in the mean sense) stochastic process to be wide-sense
stationary will be presented.
