ETS Model Calculator

Inputs

Example Data Table

Formula Used

Simple exponential smoothing (level):

• ℓ_t = α·y_t + (1−α)·ℓ_t−1
• One-step fitted value: ŷ_t|t−1 = ℓ_t−1

Trend smoothing (Holt):

• ℓ_t = α·y_t + (1−α)·(ℓ_t−1 + b_t−1)
• b_t = β·(ℓ_t − ℓ_t−1) + (1−β)·b_t−1
• Fitted value: ŷ_t|t−1 = ℓ_t−1 + b_t−1

Damped trend (with φ):

• Replace b_t−1 with φ·b_t−1 in the level update, and smooth the trend toward a smaller long-run slope.

Holt–Winters additive seasonality (length m):

• ŷ_t|t−1 = (ℓ_t−1 + φ·b_t−1) + s_t−m
• ℓ_t = α·(y_t − s_t−m) + (1−α)·(ℓ_t−1 + φ·b_t−1)
• b_t = β·(ℓ_t − ℓ_t−1) + (1−β)·(φ·b_t−1)
• s_t = γ·(y_t − ℓ_t) + (1−γ)·s_t−m

Holt–Winters multiplicative seasonality:

• ŷ_t|t−1 = (ℓ_t−1 + φ·b_t−1) · s_t−m
• Season update uses ratios: s_t = γ·(y_t/ℓ_t) + (1−γ)·s_t−m

How to Use This Calculator

1. Paste your time series values in order, one per line or comma-separated.
2. Select a model: level only, trend, damped trend, or seasonal smoothing.
3. Set smoothing factors (α, β, γ). Use 0.1–0.4 as a starting range.
4. For seasonal models, set the season length m (like 12 for monthly data).
5. Choose a forecast horizon, then press Submit to compute fitted values and forecasts.
6. Review MAE, RMSE, and MAPE to compare parameter settings, then export CSV or PDF.

Why ETS fits operational forecasting

Exponential smoothing is designed for short‑term decision cycles where recent observations carry the most information. The ETS family separates the signal into level, trend, and seasonal components, then updates each component every period. This structure makes it practical for inventory, demand, staffing, web traffic, and finance dashboards where a fast refresh matters.

Model selection and component logic

When data has no consistent direction, a level model can be sufficient. If values rise or fall steadily, trend smoothing reduces lag by estimating a slope. If growth slows over time, damping shrinks the long‑run slope so forecasts do not explode. If repeating patterns exist, additive seasonality suits stable amplitudes, while multiplicative seasonality suits proportional swings.

Interpreting α, β, γ, and φ

α controls how quickly the level reacts: higher α tracks changes faster but can chase noise. β controls how quickly the trend adapts; higher β responds to turning points but can overshoot. γ controls seasonal updates; higher γ re-learns seasonality quickly when patterns shift. φ between 0 and 1 dampens trend influence on future steps and stabilizes long horizons.

Using error metrics to tune settings

The fitted value is the one‑step‑ahead estimate for each period, and the residual is actual minus fitted. MAE summarizes typical absolute error in original units. RMSE penalizes large mistakes more heavily, which is useful when spikes are costly. MAPE expresses error as a percentage, but it is unreliable when actual values are near zero.

Practical workflow for consistent results

Start with sensible season length (m) and a moderate α such as 0.2–0.4. Add trend only if the residuals show systematic drift. Introduce damping when trend forecasts look unrealistically steep. Compare two to three parameter sets using MAE and RMSE, then lock a configuration and monitor errors monthly to detect structural change.

For monthly series, m=12 is common; for weekly seasonality in daily data, m=7. Keep horizon modest: 4–12 steps often yields better control. If you are unsure, run a small search over α, β, γ in increments of 0.05 and pick the lowest RMSE on the most recent third of observations. Then validate on the next periods before deploying widely today.

FAQs

1) What is an ETS model in forecasting?

An ETS model is a state‑space form of exponential smoothing that updates level, trend, and seasonal components each period. It produces forecasts and fitted values that adapt quickly to recent changes without needing explicit regression features.

2) How do I choose between additive and multiplicative seasonality?

Use additive seasonality when seasonal swings are about the same size in units across time. Use multiplicative seasonality when swings grow or shrink with the series level, such as sales that scale with overall demand.

3) What do MAE, RMSE, and MAPE tell me here?

MAE is the typical absolute miss in original units. RMSE penalizes large errors more, highlighting volatility risk. MAPE expresses average percentage error, but it can be misleading when actual values include zeros or very small numbers.

4) Why is a damping factor useful?

Damping reduces the long‑run effect of the trend so forecasts flatten gradually instead of extending a steep slope indefinitely. It is helpful when growth saturates, promotions end, or capacity constraints limit continued increases.

5) What season length should I enter?

Enter the number of observations in one full cycle: 12 for monthly yearly seasonality, 4 for quarterly patterns, 7 for daily data with weekly cycles, or 24 for hourly data with daily cycles.

6) Can I export and reuse the results?

Yes. The CSV export captures parameters, fitted values, residuals, and forecasts for auditing and charting. The PDF realizes the same tables for sharing, reviews, or attaching to reports and internal documentation.