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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.

enter image description here

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I think it makes sense if you can account, by citing some physical law, for example, that can support the magnitude of the observed seasonal effect.

Understanding the dynamics can be useful in predicting when the seasonality may be become somewhat muted (or intensified). It may also suggest significant auxiliary variables.

In order words, you can accompany your forecasts with rationale as to why future forecast may be off with guidance (caveats). This may also lead incidentally to the construction of a model that continues to actually perform well in time.

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  • $\begingroup$ Thanks tor Your answer. I don't understand it completely so far. Did you mean that in the current situation seasonality seem to be intensified? And that the current model's good performance is incidental? If so, is this considered a problem? And do you think it's better not ti use signal extraction to detect seasonality? $\endgroup$ – roma salah Apr 19 at 16:52

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