If you perform a classical additive decomposition, how are the components combined?

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BlackTom AI · Accepted Answer

The question asks about the classical additive decomposition and how the components are combined.
Option 1: 'Yt = Tt × St × Rt' proposes a multiplicative combination of trend, seasonal, and remainder components. In classical additive decomposition, the components are added, not multiplied, so this option misrepresents the fundamental form.
Option 2: 'Yt = Tt + St + Rt' aligns with the standard additive model, where the observed value is the sum of trend, seasonal, and irregular/remnant components. This expresses the idea that each component contributes additively to the total.
Option 3: 'Yt = Tt + St × Rt' mixes addition with multiplication between St and Rt while keeping Tt added, which deviates from the pure additive structure and introduces an inconsistency in how components should interact.
Option 4: 'Yt = (Tt + St) × Rt' presents a multiplicative interaction between the sum of trend and seasonality with the remainder, which is characteristic of a multiplicative model, not the additive one. This does not reflect the additive decomposition.
In summary, the additive decomposition model requires that the components be combined by simple addition, which is precisely what option 2 states. The other options introduce multiplication or mixed operations, contradicting the additive framework.

If you perform a classical additive decomposition, how are the components combined?

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