Calculator Inputs
Enter a seasonal time series, set smoothing factors, and generate fitted values plus forecasts.
Example Data Table
Use this quarterly demand sample to test the calculator quickly.
| Period | Quarter | Observed Value |
|---|---|---|
| 1 | Q1 | 120 |
| 2 | Q2 | 135 |
| 3 | Q3 | 150 |
| 4 | Q4 | 170 |
| 5 | Q1 | 160 |
| 6 | Q2 | 145 |
| 7 | Q3 | 130 |
| 8 | Q4 | 150 |
| 9 | Q1 | 168 |
| 10 | Q2 | 185 |
| 11 | Q3 | 176 |
| 12 | Q4 | 160 |
Formula Used
Triple exponential smoothing extends single and double smoothing by tracking level, trend, and repeating seasonal movement.
- Additive level:
Lt = α(Yt - St-m) + (1-α)(Lt-1 + Tt-1) - Additive trend:
Tt = β(Lt - Lt-1) + (1-β)Tt-1 - Additive seasonality:
St = γ(Yt - Lt) + (1-γ)St-m - Additive forecast:
Ft+h = Lt + hTt + St-m+h - Multiplicative level:
Lt = α(Yt / St-m) + (1-α)(Lt-1 + Tt-1) - Multiplicative seasonality:
St = γ(Yt / Lt) + (1-γ)St-m - Multiplicative forecast:
Ft+h = (Lt + hTt) × St-m+h - Error metrics: MAE is the mean absolute error, RMSE squares errors before averaging, and MAPE shows percentage error size.
How to Use This Calculator
- Paste your time series in exact chronological order.
- Choose the seasonal cycle length, such as 4 or 12.
- Set alpha, beta, and gamma between 0 and 1.
- Select additive or multiplicative seasonality based on your data pattern.
- Enter how many future periods you want to forecast.
- Press Submit to calculate fitted values and forecasts above the form.
- Review MAE, RMSE, MAPE, and the detailed tables.
- Use the CSV or PDF buttons to export results.
Frequently Asked Questions
1. What does triple exponential smoothing measure?
It models three components together: the baseline level, the long-term trend, and the repeating seasonal pattern. This makes it useful for cyclical time-series forecasting.
2. When should I choose additive seasonality?
Choose additive seasonality when seasonal swings stay roughly the same size over time. Sales rising by about 20 units every winter is a common additive pattern.
3. When is multiplicative seasonality better?
Use multiplicative seasonality when seasonal effects grow or shrink with the series level. For example, peak months doubling as the business grows fits this style.
4. How much history should I enter?
At least two complete seasons are recommended, but more history usually improves stability. Twelve to twenty-four periods often work well for monthly data.
5. How do alpha, beta, and gamma affect results?
Higher values react faster to recent changes. Lower values smooth more aggressively and resist noise. Tuning them helps balance responsiveness against stability.
6. Why are my first fitted values blank?
The model needs an initial season to estimate starting level, trend, and seasonal factors. Because of that setup, the first season acts as calibration data.
7. What do MAE, RMSE, and MAPE tell me?
They show forecast accuracy from different angles. MAE gives average absolute error, RMSE penalizes larger misses, and MAPE shows relative percentage error.
8. Can I use this for non-seasonal data?
You can, but a simpler smoothing method is usually better when seasonality is absent. This calculator is designed for repeating seasonal behavior.