Calculator Inputs
Formula Used
Simple Moving Average
SMAt = (xt-1 + xt-2 + ... + xt-n) / n
Weighted Moving Average
WMAt = Σ(wixt-i) / Σwi
Exponential Moving Average
EMAt = αxt + (1 − α)EMAt-1
Moving averages mainly estimate a local level. Trend and seasonal settings extend that behaviour.
How to Use
- Enter ordered observations or upload a valid CSV file.
- Select a moving-average method and suitable window size.
- Choose preprocessing, validation, and advanced forecasting options.
- Calculate, compare accuracy metrics, and inspect forecast intervals.
- Copy results or export the table, chart, and report.
Example Data
| Month | Observed demand | Purpose |
|---|---|---|
| January | 120 | Starting observation |
| February | 128 | Second observation |
| March | 125 | Completes a three-period window |
| April | 134 | First one-step forecast comparison |
Frequently Asked Questions
What is a moving average forecast?
It predicts future values using averages of recent observations. The window controls responsiveness and smoothness.
How should I choose the window size?
Use smaller windows for fast changes. Use larger windows for smoother, slower patterns.
When should I use WMA?
Use WMA when recent observations should influence forecasts more strongly. Custom weights define that influence.
How is EMA different from SMA?
EMA applies exponentially declining weights. It usually reacts faster than an equal-weight SMA.
What does RMSE measure?
RMSE measures typical forecast error while penalising large misses more heavily. Lower values are better.
Why can MAPE be unavailable?
MAPE divides errors by actual values. Zero actual values make that percentage undefined.
Does a moving average model trends?
A basic moving average estimates level only. Enable trend adjustment or double moving averages for trend.
What is walk-forward validation?
It repeatedly forecasts the next observation using earlier data. This helps prevent future-data leakage.
Are forecast intervals guaranteed?
No. These intervals use historical residual error assumptions. Structural changes can reduce their reliability.