Removing seasonality in time series forecasting

Question

In time series forecasting we are removing the "seasonal" component to fit models better and have better forecasting. But why? if I should give an extreme example: if I have a sin wave, I wouldn't remove the seasonal component of it. Because it is much easier to forecast with its own structure (because it has an easily recognizable pattern). Am I wrong?

Answer 1

Removing seasonality is not something you are obliged to do. It really depends on the model. The idea of decomposing time series (you are not actually removing seasonality, it is simply a component you analyse in a different way) comes from the fact that you model your time series as a sum (or product) of contributions

$$\psi(t) = \psi_s(t) + \psi_\tau(t) + \varepsilon(t)\, .$$

In order to forecast the future behaviour the only "unmodelled" part is the $\varepsilon$ component, hence you already know how to forecast the trend and seasonality parts. So, a first forecast model might be created by decomposing the series and model trend and seasonality.

This, however, comes from the chosen model, meaning your hypothesis is that your time series is actually decomposable as above (with $\varepsilon$ following a normal distribution).

On the other hand, if you model your series otherwise, like with a Deep Learning model you do not need (and it is generally not advisable) to decompose the series into components.