The Holt-Winters additive model applies to time series whose amplitude increases or decreases over time.

Question

BlackTom AI · Accepted Answer

The Holt–Winters additive form assumes seasonal effects are constant in magnitude regardless of the series level; if the seasonal amplitude grows or shrinks with the level, the multiplicative form is appropriate.

1) Relevant knowledge points and concepts
- Holt–Winters (also called triple exponential smoothing) models three components: level (l_t), trend (b_t), and seasonal (s_t).
- Two common variants: additive and multiplicative. The additive variant models seasonality as an additive term of roughly constant size; the multiplicative variant models seasonality as proportional to the level (i.e., amplitude changes as the series level changes).

2) Step-by-step reasoning
- Additive forecast equation: ŷ_{t+h} = l_t + h b_t + s_{t+h-m}. Here s_{·} adds a fixed seasonal amount to the baseline (level + trend).
- Multiplicative forecast equation: ŷ_{t+h} = (l_t + h b_t) × s_{t+h-m}. Here s_{·} scales the baseline, so seasonal amplitude changes proportionally with the level.
- If the observed seasonal swings become larger as the series grows (or smaller as it declines), the multiplicative form captures that behavior; the additive form does not.

3) Intermediate expressions (explicit)
- Additive: forecast = l_t + h b_t + s_{t+h-m}
- Multiplicative: forecast = (l_t + h b_t) × s_{t+h-m}

4) Why the correct answer is correct
- The statement claims the additive model applies when amplitude increases or decreases over time. Because additive seasonality is constant in magnitude, it cannot model amplitude that changes with level; that is exactly what the multiplicative model is designed for. Therefore the statement is false.

5) Why the other option is incorrect
- Choosing "True" would imply additive seasonality handles changing amplitude; that is incorrect—using an additive model when seasonality is proportional to level produces biased forecasts and poor fit.

6) Conclusion
- The correct answer is False, which matches the provided answer.

The Holt-Winters additive model applies to time series whose amplitude increases or decreases over time.判断题

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