Exponential smoothing
Holt–Winters forecast with an additive trend and an optional seasonal period.
When to use it
Use exponential smoothing when you want a Holt–Winters forecast of one numeric series: a level, an additive trend, and (when the series is long enough) an additive seasonal term. ARIMA of the same series is ARIMA / SARIMA.
Assumptions
The target is numeric, with at least eight non-missing values. Seasonal period starts at 12. Additive season is used only when the series is at least twice that period; otherwise the fit is trend only. The 95% interval is residual SD times 1.96, not a model-based prediction interval.
Running it in Tensr
Options
Prop
Type
Reading the output
The same 48 months of sales. Holt–Winters with period 12 and an additive trend. The series is long enough for additive season.
| Step | Forecast | Lower 95% | Upper 95% |
|---|---|---|---|
| 1 | 47.7512 | 42.4977 | 53.0047 |
| 2 | 50.9862 | 45.7327 | 56.2397 |
| 3 | 51.0988 | 45.8453 | 56.3522 |
| 4 | 53.7263 | 48.4728 | 58.9798 |
| 5 | 51.8013 | 46.5478 | 57.0548 |
| 6 | 49.3238 | 44.0703 | 54.5773 |
| 7 | 50.0013 | 44.7478 | 55.2548 |
| 8 | 44.8363 | 39.5828 | 50.0898 |
Period = 12, SSE = 344.846, N = 48. The interval is residual SD × 1.96, so a wide band means the fit left a lot of leftover scatter, not a model-based prediction interval.
Reporting (APA 7)
Holt–Winters exponential smoothing of monthly sales, N = 48, period = 12. Report the forecast and the approximate interval.
Coming from SPSS
SPSS is Analyze → Forecasting → Create Models with exponential smoothing. Tensr’s item is Time series → Forecasting → Exponential Smoothing. The path string stored for this item says Time series → Forecasting → Holt-Winters.
SPSS can choose additive or multiplicative season. Tensr is additive trend, and additive season when the series is long enough.
Related
ARIMA / SARIMA is the other forecast. STL is the decomposition without a forecast.