In a non-stationary time series of order=1 I first remove seasonality by 1) automatic detection of frequencies with high power then 2) multiplying it by a moving avergae of the time series.
I then subtract the weighted seasonal trend, difference, forecast with ARMA, simulate seasonal trend for the forecasted points and sum it to the ARMA forecasts.
Now my ARMA foreacast look very weird as in the plot here. The forecasts are super smooth (right end of the plot), barely changing in value from one point to the next, while the detrended series (left side of the plot) still looks cyclical.
Do theses forecasts look normal to you? considering that, I'm actually getting pretty accurate forecasts after I add the simulated seasonal waves.