In exponential smoothing, a large smoothing constant 𝛼 (e.g., close to 1) means:

Question

BlackTom AI · Accepted Answer

The single-equation form Ft+1 = α Xt + (1 − α) Ft immediately shows the key role of α: it is the weight placed on the most recent observation Xt while (1 − α) is the weight carried forward from the previous forecast.

1. Relevant knowledge points and concepts
- Exponential smoothing assigns exponentially decaying weights to past observations.
- α (0 < α ≤ 1) is the smoothing constant: larger α gives more weight to recent data and makes forecasts more responsive; smaller α spreads weight more evenly over older observations and yields smoother forecasts.
- The weight on the observation k periods ago is α(1 − α)^k, and the infinite series of weights sums to 1.

2. Step-by-step reasoning
- Start from Ft+1 = α Xt + (1 − α) Ft.
- Recursively substitute Ft = α Xt−1 + (1 − α) Ft−1 to reveal weights:
  Ft+1 = α Xt + α(1 − α) Xt−1 + α(1 − α)^2 Xt−2 + ... .
- Thus the immediate weight on Xt is α; on Xt−1 is α(1 − α); on Xt−2 is α(1 − α)^2, etc.

3. Calculations and intermediate steps
- General weight k periods back: wk = α(1 − α)^k.
- Sum of weights: Σ_{k=0 to ∞} α(1 − α)^k = α / [1 − (1 − α)] = α / α = 1 (weights normalize to 1).
- Example: α = 0.9 → weights: X_t: 0.9; X_{t−1}: 0.9×0.1 = 0.09; X_{t−2}: 0.009, etc. Almost all weight is on recent values.
- Example: α = 0.1 → weights: X_t: 0.1; X_{t−1}: 0.09; X_{t−2}: 0.081, etc. Weight is spread more to older data.

4. Why the correct answer is correct
With α close to 1, α is large so the weight α on the most recent observation dominates, and (1 − α) is small so weights on older observations rapidly shrink. That directly means the forecast places more weight on recent observations and reacts quickly to new changes.

5. Why other options are incorrect
- “Equivalent to a simple moving average”: incorrect because SMA gives equal weight over a fixed window while exponential smoothing gives geometrically decreasing weights.
- “There is no effect on responsiveness”: incorrect because α explicitly controls responsiveness.
- “Places almost all weight on older historical data”: incorrect — the opposite is true when α is large.

6. Conclusion
Therefore the correct choice is: "The forecast places more weight on recent observations." This matches the provided answer.

In exponential smoothing, a large smoothing constant 𝛼 (e.g., close to 1) means:单项选择题

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