In the textbook *Forecasting: principles and practice* by Hyndman and Athanasopoulos, in the Classical Decomposition (Sec 6.3), in step 3 of the additive decomposition algorithm, the authors state that the seasonal indexes have to be adjusted to ensure that they add to zero. Why is that?

Any help would be appreciated.

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#### Best Answer

Just to make coefficients meaningful. Suppose you had quarterly data and a pattern within the year. If you include a year effect the seasonal coefficients can be interpreted as average deviations from the year average, and as such should add up to zero. It is just the same reason why ANOVA effects are made to add up to zero as well.

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