Smoothing · Free
Simple exponential smoothing
A fading memory of the local level — no trend, no season.
What it assumes
Local level only; no trend, no season.
When to use
Stable or slowly changing mean; intermittent-adjacent smooth series.
When to avoid
Trend or seasonality. On spare parts with zeros, prefer Croston.
Knobs
l_t = α y_t + (1−α) l_{t−1}. α is grid-searched on SSE.
How it works
Simple exponential smoothing updates a level: ℓ_t = α y_t + (1−α) ℓ_{t−1}. The forecast is that level for every horizon. α near 1 trusts the latest point (almost naive); α near 0 is very smooth. The engine grid-searches α on SSE. SES is the workhorse for a stable mean. Trend or season need Holt or Holt–Winters; many zeros need the Croston family.
Sample forecast question
Given these eight Monday call counts, what is the simple-exponential-smoothing forecast for the next three Mondays?
Step-by-step on these numbers
| Period | Actual | Fitted |
|---|---|---|
| M1 | 19 | 19 |
| M2 | 21 | 19 |
| M3 | 18 | 19.40 |
| M4 | 20 | 19.12 |
| M5 | 22 | 19.30 |
| M6 | 19 | 19.84 |
| M7 | 20 | 19.67 |
| M8 | 21 | 19.74 |
| Period | Forecast | 95% interval |
|---|---|---|
| M9 | 19.99 | 17.28 – 22.70 |
| M10 | 19.99 | 16.15 – 23.82 |
| M11 | 19.99 | 15.29 – 24.69 |
Parameters the engine found
alpha= 0.200last= 19.988
The question
Given these eight Monday call counts, what is the simple-exponential-smoothing forecast for the next three Mondays? Sample mondays: M1=19, M2=21, M3=18, M4=20, M5=22, M6=19, M7=20, M8=21 (calls).
Level recurrence
ℓ_t = α y_t + (1−α) ℓ_{t−1}, with ℓ_0 = y_1 = 19. The h-step forecast is the last level.
Pick α
The engine grid-searches α ∈ {0.05, 0.10, …, 0.95} on in-sample SSE. Winner: α = 0.200.
First updates
t=1: forecast 19 against y=19, then ℓ = 0.200×19 + 0.800×19 = 19. t=2: forecast 19 against y=21, then ℓ = 0.200×21 + 0.800×19 = 19.40. t=3: forecast 19.40 against y=18, then ℓ = 0.200×18 + 0.800×19.40 = 19.12.
Last level
After the full sample, ℓ_n = 19.99 (engine last = 19.99). Forecast: M9: 19.99; M10: 19.99; M11: 19.99.
Interval
Residual σ = 1.384. For h = 1 the 95% band is [17.28, 22.70] around 19.99. The engine labels this interval native for the method.
Graph of this sample
The chart plots the canned table on this page (actuals, in-sample fitted, forecast, 95% interval). Not your Excel series. Free analysis never uploads raw data.
Educational only. Not investment, weather, or operational advice. In the add-in, rank is rolling-origin MASE — “best supported among candidates on this series.”