In the recent X-12-ARIMA program developed by the United States Census Bureau for seasonal adjustments,the RegARIMA modeling has been extensively utilized.We shall discuss some problems in the RegARIMA modeling when the time series are realizations ofnon-stationary integrated stochastic processes.We propose to use the seasonal switching autoregressive moving average (SSARMA) model and the regression SSARMA (RegSSARMA)model to cope with seasonalities commonly observed in many economic time series.