Q.Explain the additive and multiplicative models used to describe a time series. When is each considered appropriate?

The four components of a time series can be combined either by simple addition or by multiplication, and the right choice depends on how the fluctuations behave as the trend level changes. …

A time series' four components — Trend ($T$), Seasonal ($S$), Cyclical ($C$), and Irregular ($I$) variation — can be combined in two classical ways.

Additive model:

Here all four components are expressed in the same original units as $Y$, and they are assumed to act independently of each other, so the absolute size of the seasonal and cyclical swings stays roughly the same regardless of whether the trend level is high or low. This model is appropriate when a plotted series shows fluctuations of roughly constant absolute width around the trend, whatever the trend's level.

Multiplicative model:

$Y = T \times S \times C \times I$ …

Assuming the additive model is always simpler and therefore always right — the choice must be based on whether the data's fluctuations look constant in absolute size (additive) or grow …