Calculator
Example Data Table
This sample series represents monthly demand values. Copy the values into the calculator to test different methods and horizons.
| Period | Value |
|---|---|
| Jan | 120 |
| Feb | 128 |
| Mar | 133 |
| Apr | 129 |
| May | 141 |
| Jun | 150 |
| Jul | 155 |
| Aug | 160 |
| Sep | 158 |
| Oct | 166 |
| Nov | 172 |
| Dec | 180 |
Formula Used
Simple Moving Average (SMA)
Forecast = (1/k) × Σ last k values
Use SMA when the series is stable and noise dominates. Larger k smooths more but reacts slower.
Weighted Moving Average (WMA)
Forecast = Σ(wᵢ×yᵢ) / Σwᵢ
Use WMA when recent observations should matter more. Increasing weights makes the forecast more responsive.
Simple Exponential Smoothing (SES)
ℓₜ = αyₜ + (1−α)ℓₜ₋₁, Forecast = ℓₜ
SES suits level-only series. Higher α tracks changes faster; lower α smooths more.
Holt Trend (Linear)
ℓₜ = αyₜ + (1−α)(ℓₜ₋₁+bₜ₋₁)
bₜ = β(ℓₜ−ℓₜ₋₁) + (1−β)bₜ₋₁
h-step Forecast = ℓₜ + h·bₜ
Holt is best when a trend exists but seasonality is weak. Use error metrics to compare against SES and averages.
How to Use This Calculator
- Paste your time series values in chronological order.
- Select a method: averages for stability, smoothing for drift, Holt for trend.
- Set horizon and model settings (window, alpha, beta, optional weights).
- Press Submit to display forecasts above the form.
- Compare MAE, RMSE, and MAPE across methods to choose the best fit.
- Download CSV or PDF to share results and track revisions.
Insights Article
Method selection and data behavior
This calculator supports moving averages, exponential smoothing, and linear trend smoothing. Moving averages suit series with low drift and consistent variance, while smoothing methods adapt faster to level changes. Holt trend is preferred when the latest values show a persistent slope. If your series contains abrupt interventions, test both a responsive setting and a smoother setting to see which minimizes error. Always compare methods on the same horizon to keep decisions consistent.
Window length and responsiveness trade‑offs
The window parameter controls how much history influences the average forecast. A short window reacts quickly but can overfit noise, increasing forecast volatility. A longer window reduces variance and stabilizes projections, but may lag behind turning points. When values are autocorrelated, a slightly longer window can reduce oscillation and produce steadier plans. Review the fitted behavior as well as the next-step forecast to confirm realism.
Alpha and beta tuning for smoothing models
In smoothing, alpha governs how strongly new observations update the level. Higher alpha follows recent values, while lower alpha emphasizes the existing level estimate. For Holt, beta updates the trend component; higher beta responds faster to slope changes. Start with alpha 0.2–0.5 and beta 0.1–0.3, then adjust based on RMSE and MAPE. If the trend flips direction often, lower beta to avoid chasing short runs.
Interpreting MAE, RMSE, and MAPE
MAE reports the typical absolute miss in the same units as the data. RMSE penalizes large misses and is useful when spikes are costly. MAPE expresses average error as a percentage, enabling comparisons across scales, but it becomes unstable near zero values. For business reporting, MAE is often easiest to translate into impact, while RMSE helps quantify risk from rare but large errors. Use at least two metrics to avoid choosing a method for one favorable statistic only.
Forecast intervals and decision confidence
The interval bounds use residual dispersion and expand with the square root of the forecast step, reflecting rising uncertainty further into the future. Narrow intervals suggest stable behavior, while wide intervals signal volatility or poor model fit. If bounds are persistently wide, shorten the horizon, recheck outliers, or segment the series by regime before modeling. Treat intervals as operational guardrails: they help set reorder points, staffing buffers, and service targets when variability matters.
FAQs
1) How many data points should I enter?
Use at least 12 points when possible. More history improves smoothing stability and makes error metrics more reliable. For Holt, 4+ points are recommended to estimate a meaningful trend.
2) Which method is best for a flat series?
If the series has a stable level with random noise, choose SES or SMA. SES adapts to gradual shifts, while SMA is intuitive and easy to communicate in reports.
3) When should I use weighted averages?
Use WMA when recent observations should influence forecasts more than older ones. Increasing weights toward the latest values improves responsiveness without introducing a trend component.
4) What do alpha and beta actually change?
Alpha controls how quickly the level updates after each observation. Beta controls how quickly the trend updates in Holt. Higher values respond faster but can amplify noise and reduce stability.
5) Why can MAPE look high on small numbers?
MAPE divides by the actual value, so near‑zero observations can inflate percentages. In such cases, rely more on MAE or RMSE, and consider transforming data if appropriate.
6) How should I use the interval bounds?
Treat bounds as a planning range, not a guarantee. If your operational decision requires a conservative estimate, plan with the lower bound for capacity or the upper bound for demand, depending on risk.