In time series decomposition, under an additive model, how is the seasonality component applied to the trend?

In time series decomposition, under an additive model, how is the seasonality component applied to the trend?

• A. Multiplied with the trend
• B. Added to the trend
• C. Subtracted from the trend
• D. Divided into the trend

Answer: (B)

Under an additive time series decomposition, the components simply add up: observed = trend + seasonal + residual. The seasonality is a fixed amount that is added to the underlying trend for each period, not scaled or multiplied. So the seasonality is applied to the trend by adding its seasonal amount to the trend value. For example, if the trend is 100 and the seasonal effect for a period is +8, the observed value is 108 (plus any residual). If the seasonal effect is -6, the observed value is 94. This contrasts with a multiplicative model, where seasonality would multiply the trend (observed = trend × seasonal × residual).

Under an additive time series decomposition, the components simply add up: observed = trend + seasonal + residual. The seasonality is a fixed amount that is added to the underlying trend for each period, not scaled or multiplied. So the seasonality is applied to the trend by adding its seasonal amount to the trend value. For example, if the trend is 100 and the seasonal effect for a period is +8, the observed value is 108 (plus any residual). If the seasonal effect is -6, the observed value is 94. This contrasts with a multiplicative model, where seasonality would multiply the trend (observed = trend × seasonal × residual).