Smoothing methods forecast by giving more weight to recent observations. Choose a moving average, simple exponential smoothing, Holt’s trend method or Holt-Winters for seasonal data, and compare their in-sample accuracy.
How it works
Forecast a time series with simple or weighted moving averages, simple exponential smoothing, Holt’s trend method or Holt-Winters seasonal smoothing, and compare in-sample accuracy.
SMA: F(t+1) = average of the last w actuals
WMA: weights 1, 2, …, w with the most recent weighted highest
SES: L(t) = α·Y(t) + (1 − α)·L(t−1); F = L(t)
Holt: L(t) = α·Y(t) + (1 − α)(L + B); B(t) = β(L(t) − L(t−1)) + (1 − β)B(t−1); F(k) = L + k·B
Holt-Winters adds S(t) = γ(Y(t) − L(t)) + (1 − γ)S(t − m); F(k) = L + k·B + SCommon uses
- Short-term demand and volume forecasting
- Revenue and expense forecasts between budget cycles
- Teaching and comparing forecasting methods
Worked example
The calculator above opens with this example. Change any input to see the results update instantly, or select Reset to return to these figures.
| Time series (oldest first) | 412 398 436 445 468 452 441 459 487 503 498 541 455 437 481 492 515 501 487 506 535 556 549 597 |
| Method | Holt-Winters (additive seasonality) |
| Alpha (level) | 0.3 |
| Beta (trend) | 0.1 |
| Gamma (seasonal) | 0.2 |
| Season length (periods) | 12 |
| Periods to forecast | 6 |
| Next-period forecast | 483.02 |
| Average of next 6 periods | 511.83 |
| MAPE (in-sample) | 2.6% |
| MAE | 12.96 |
| RMSE | 15.74 |
| Fitted periods | 12 |
Accuracy is measured on one-step-ahead fitted values; compare methods on the same series and choose the lowest error that still makes business sense.
Interpreting the results
- Moving averages and simple smoothing lag behind trends; use Holt for trending data and Holt-Winters when seasonality repeats.
- Higher alpha reacts faster to recent changes but also chases noise; values between 0.1 and 0.4 are typical.
- Hold out the most recent periods, forecast them, and compare against actuals before relying on a model.
Frequently asked questions
Which smoothing method should I use?
Use a moving average or simple exponential smoothing for stable series without trend, Holt’s method when the series trends steadily, and Holt-Winters when a seasonal pattern repeats every year or quarter.
How do I choose alpha, beta and gamma?
Higher values react faster to recent changes, while lower values smooth out noise. Start between 0.1 and 0.3, then compare in-sample errors such as MAPE and choose the combination that is accurate without overreacting.
How much data does Holt-Winters need?
Holt-Winters needs at least two full seasonal cycles to initialize the seasonal factors, which means 24 months for monthly data or 8 quarters for quarterly data. Three or more cycles give more reliable estimates.
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