Moving Average
Smooth a series into arithmetic means over overlapping fixed-size windows.
Description
Smooth a numeric series with overlapping simple arithmetic-mean windows.
A simple moving average reduces short-term variation by replacing each complete window with its mean. It is useful for trend inspection, sensor summaries, and understanding the effect of a fixed rolling window.
When to use Moving Average Calculator
- Smooth a noisy ordered series
- Compare trends at different window widths
- Summarize each complete sliding window
How the calculation works
For width w, the first output averages values 0 through w−1 and each later output moves one position. No partial windows or padding are used, so n inputs produce n−w+1 averages.
MAₜ = (xₜ₋w₊₁ + … + xₜ) / w Interpreting the result
Larger windows smooth more strongly but delay and blur changes. Output positions align with completed windows rather than directly with the first observations unless the caller supplies its own timestamps.
Important limitations
- The series must contain at least one complete window.
- All observations receive equal weight.
- Missing values, irregular time spacing, and edge padding are not modeled.