Smoothing · Free
Damped trend
A trend that flattens (φ < 1) instead of running forever.
What it assumes
Trend that flattens toward a constant (φ < 1).
When to use
Growth that should not be extrapolated linearly forever.
When to avoid
A truly linear long trend, or strong seasonality.
Knobs
α, β, and damping φ ∈ (0,1].
How it works
Damped trend is Holt with a brake: each future step of the trend is multiplied by φ ∈ (0,1]. The forecast approaches a horizontal line. That is usually more honest for products that launch fast and then mature. A truly linear long trend may prefer Holt; strong season still needs Holt–Winters.
Sample forecast question
Downloads grew quickly, then the slope faded. What is the damped-trend forecast for the next four months?
Step-by-step on these numbers
| Period | Actual | Fitted |
|---|---|---|
| Jan | 8 | 11.20 |
| Feb | 12 | 11.76 |
| Mar | 15 | 13.90 |
| Apr | 17 | 16.18 |
| May | 19 | 17.99 |
| Jun | 20 | 19.67 |
| Jul | 21 | 20.74 |
| Aug | 21 | 21.60 |
| Period | Forecast | 95% interval |
|---|---|---|
| Sep | 21.79 | 19.04 – 24.53 |
| Oct | 22.22 | 18.34 – 26.11 |
| Nov | 22.57 | 17.82 – 27.33 |
| Dec | 22.85 | 17.36 – 28.35 |
Parameters the engine found
alpha= 0.600beta= 0.050phi= 0.800level= 21.239trend= 0.684
The question
Downloads grew quickly, then the slope faded. What is the damped-trend forecast for the next four months? Sample months: Jan=8, Feb=12, Mar=15, Apr=17, May=19, Jun=20, Jul=21, Aug=21 (downloads (00s)).
Brake on the trend
Same level/trend updates as Holt, but each future step of the slope is multiplied by φ ∈ (0,1]. The path bends toward a plateau.
Weights
Grid search on this sample: α = 0.600, β = 0.050, φ = 0.800. End states: ℓ = 21.24, b = 0.68.
Forecast rule
ŷ_{n+h} = ℓ + (φ + φ² + … + φ^h) b. Path: Sep: 21.79; Oct: 22.22; Nov: 22.57; Dec: 22.85.
Interval
Residual σ = 1.401. For h = 1 the 95% band is [19.04, 24.53] around 21.79. 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.”