Calculator
Paste a numeric time series, choose smoothing settings, then generate fitted values and forecasts.
Example data table
Sample monthly demand series with an upward trend. Try copying these values into the calculator.
| Month | Value | Notes |
|---|---|---|
| Jan | 120 | Base level |
| Feb | 128 | Trend begins |
| Mar | 133 | Steady growth |
| Apr | 140 | Higher demand |
| May | 151 | Acceleration |
| Jun | 160 | Sustained rise |
| Jul | 172 | Season-neutral series |
| Aug | 181 | Continued trend |
| Sep | 190 | Moderate increase |
| Oct | 205 | Demand spike |
| Nov | 219 | Stabilizing |
| Dec | 230 | Year-end high |
Formula used
This calculator uses Holt’s linear trend model (double exponential smoothing):
- Ft = Lt-1 + Tt-1 (one-step fitted forecast)
- Lt = αYt + (1-α)(Lt-1 + Tt-1)
- Tt = β(Lt − Lt-1) + (1-β)Tt-1
- Forecast: Ŷt+m = Lt + mTt
α controls how quickly the level updates; β controls how quickly the trend updates.
How to use this calculator
- Paste your numeric series in order (oldest to newest).
- Start with α = 0.3 and β = 0.2, then adjust.
- Set forecast periods to match your planning horizon.
- Use regression initialization for smoother early values.
- Review MAE/RMSE/MAPE to compare settings objectively.
- Export CSV for deeper analysis, or PDF for sharing.
Data requirements and structure
Use evenly spaced observations with a clear trend. Enter values oldest to newest and keep one unit, like revenue or demand. Prefer 12 to 30 points; fewer than 6 points can make the starting trend unstable. If a period is missing, do not shift dates; fill or remove consistently. A simple check is first versus last value; if change is tiny, a trend model may not help.
Choosing alpha and beta
Alpha updates the level; beta updates the trend. Start at alpha 0.30 and beta 0.20, then tune. Lower alpha to 0.15 when noise is high. Raise alpha toward 0.45 when changes are real and fast. Increase beta when the slope changes quickly, and reduce beta when forecasts overshoot.
Interpreting level and trend outputs
Level is the smoothed baseline, and trend is the smoothed change per period. If level is 200 and trend is 5, the next forecast is about 205. A near zero trend implies stability, while negative trend implies decline. Large early shifts often come from initialization, so focus on later rows.
Evaluating accuracy with error metrics
MAE is the average absolute one step error in original units. RMSE penalizes large misses and is useful when big errors are costly. MAPE is percentage based and compares across scales, but it fails near zero. As a guide, MAPE under 10% is strong, 10 to 20% is good, and above 50% needs review. Compare settings using the final 3 to 5 points as a holdout. This improves stability.
Forecast horizon and practical planning
Forecasts extend as a straight line: each step adds one trend increment. Short horizons, like 3 to 6 periods, are usually safer. Long horizons can drift if trends change. Refresh the model when new data arrives, or shorten the horizon for conservative planning. Run two parameter sets to create a simple best and worst range.
Export workflow for reporting
Use CSV to audit every row, recreate charts, and compare runs. Use PDF to share assumptions, parameters, and headline forecasts. Record alpha, beta, horizon, and any data cleaning rules with the dataset. If your series is seasonal, use a seasonal method first, then compare errors on the same holdout window.
FAQs
What is double exponential smoothing used for?
It forecasts time series that trend upward or downward without explicit seasonality. It smooths the level and the trend, then projects future values linearly from the latest estimates.
How many data points should I enter?
Two values are the minimum, but 12 to 24 points often produce steadier trend estimates. More history helps when the series is noisy or has recent anomalies.
How do I pick alpha and beta quickly?
Start near alpha 0.3 and beta 0.2, then compare MAE or RMSE across a few trials. Increase alpha for faster response; increase beta if the trend changes rapidly.
Why is MAPE shown as n/a sometimes?
MAPE requires nonzero actual values. If some actual values are zero, percentage errors can be undefined or misleading. In those cases, rely more on MAE and RMSE.
What does the fitted line represent?
It is the one-step-ahead forecast for each period, computed before updating the level and trend with the actual value. It helps you assess in-sample tracking and errors.
Can this model handle seasonality?
Not directly. It models a trend but assumes no repeating seasonal pattern. For monthly or weekly seasonality, use a seasonal extension and compare results on a holdout set.