How this calculation works
Average the latest complete window of k observations. Slide the window one period at a time and compare each forecast with the next actual when available. The final window produces the next unknown period forecast.
Forecast for t+1 = mean of yₜ₋ₖ₊₁ through yₜA worked example
With observations 10,20,30,40 and a three-period window, the forecast for period four was 20 while its actual was 40. The next-period forecast is (20+30+40)/3 = 30.
Good to know
Chronological, equally spaced unweighted data. A window of one is the last-value forecast. No calendar parsing, centered smoothing, automatic seasonality, trend extrapolation or prediction interval. Final future forecast is not scored.
Reference: NIST: moving averages (opens in a new tab) ↗
The forecast must precede the observation it predicts
For the series 10,20,30,40 and window three, the first available forecast is for period four. Only periods one through three were known at that point, so that forecast is 20. The actual fourth observation is 40 and the absolute forecast error is 20.
After observing period four, discard 10 and average 20,30,40. The resulting 30 predicts period five, whose actual has not been entered. It is reported as a future forecast and excluded from the historical error score. This separation avoids scoring a number against information that was used to calculate it.
The forecast error calculator compares aligned predictions with actuals using several error definitions. This page supplies only one-step MAE for its own available predictions.
A wider window trades responsiveness for smoothing
A one-period window repeats the latest observation and acts as a last-value baseline. Increasing the window mixes more older observations into each mean. A sudden level change then influences the forecast gradually as earlier values leave the window.
For the same rising series, windows one, two and three produce next forecasts 40,35 and 30. This does not establish that the smallest window is always best. Compare forecasts on the same later observations, rather than treating scores from different numbers of scored periods as a controlled contest.
Row positions stand for equal time intervals
The calculation has no timestamp field. If monthly data skip a month, two neighboring entries are no longer one equal time interval apart. Decide how to handle missing periods before using the model; inserting zero would assert an actual zero observation, not represent an unknown value.
The simple exponential smoothing calculator gives older observations declining influence instead of dropping them at a hard window boundary. Use the forecast error calculator to compare aligned forecasts on a deliberately chosen holdout period. No averaging window here automatically corrects a trend or seasonal cycle.
A few questions, answered
Is this a centered moving average?
No. Every window is trailing and uses only periods before the forecast period.
What if the window equals my list length?
There is one next-period forecast and no observed later period to score, so MAE is undefined.
Are the output periods calendar dates?
No. They are one-based row positions in the entered equally spaced sequence.