After decomposing a monthly time series of retail sales with tslm(), the seasonal component for March is 1.15 in a additive model. How is this value interpreted?

Question

BlackTom AI · Accepted Answer

To interpret a seasonal component from an additive time series model, we consider the seasonal effect as an absolute addition to the baseline level, measured in the same units as the series.
Option A: 'Sales in March are, on average, 15% higher than the baseline.' This would be true if the model were multiplicative and expressed as a percentage; since the model is additive, percentages are not the correct interpretation of the 1.15 value.
Option B: 'Sales in March are, on average, 115% higher than the baseline.' This overstates the effect; 1.15 in an additive model translates to 1.15 units, not a percentage of the baseline, so 115% is not the correct interpretation.
Option C: 'Sales in March are, on average, 1.15 units higher than the baseline.' This correctly reflects an additive seasonal component: March adds 1.15 units to whatever the baseline (seasonally adjusted or trend) level is, on average.
Option D: 'The seasonality increases sales by 1.15% in March.' This would imply a percentage change, which is characteristic of a multiplicative model, not an additive one; hence it is not correct for an additive seasonal term.
In summary, among additive-model interpretations, the appropriate reading of a 1.15 seasonal component is an absolute increase of 1.15 units in March, relative to the baseline level.

After decomposing a monthly time series of retail sales with tslm(), the seasonal component for March is 1.15 in a additive model. How is this value interpreted?

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