# How's the seasonal adjusted series calculated in Holt Winters method?

In the text book Forecasting: Principles and Practice in Exponential Smoothing chapter there is this part

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".. With the additive method, the seasonal component is expressed in absolute terms in the scale of the observed series, and in the level equation the series is seasonally adjusted by subtracting the seasonal component."

I'd like to know what method is used to calculate the seasonal component in order to get the seasonaly adjusted series for the level equation.

Different methods are discussed in the book like: classical decompositon, STL.. but there is no details about how it's done in the Holt-Winters forecasting method.

All flavors of Exponential Smoothing (Holt-Winters is one special case) work in the same way. You work with fixed smoothing parameters (typically denoted with Greek letters, $$\alpha$$, $$\beta$$ and $$\gamma$$) and different components (e.g., a level components $$\ell$$, a trend component $$b$$ and a set of seasonal components $$s$$).
In any case, once you have the smoothing parameters and the initial components, you walk through your time series and update the components based on the actual observations. Each Exponential Smoothing model will have its own set of updating formulas. On the FPP2 page you linked, it's right under the heading "Holt-Winters' additive method". You first update $$\ell_t$$ based on the actual observation $$y_t$$, the relevant seasonal index $$s_{t-m}$$ from one seasonal cycle back, and the previous level $$\ell_{t-1}$$ and the previous trend $$\b_{t-1}$$. Then you update the trend component $$b_t$$ and finally the seasonal component $$s_t$$.
If you then want a deseasonalized series, you just subtract $$s_t$$ from $$y_t$$.