Moving average

A moving average smooths a time series by replacing each point with the average of that point and a fixed number of the periods around or before it, sliding that window forward one step at a time. A 7-day moving average of daily signups, for instance, replaces each day's raw count with the average of the trailing seven days, damping day-to-day noise so the underlying trend is easier to see.

The simple moving average weights every point in the window equally; variants like the exponential moving average instead give more weight to recent observations, reacting faster to genuine changes at the cost of more noise, which relates it to a general weighted average. Choosing the window length is a trade-off: a short window tracks recent changes closely but stays noisy, while a long window is smoother but slower to reflect a real shift.

Moving averages matter for reading noisy operational and financial metrics, spotting trend direction, and building simple forecasting or anomaly detection baselines. A key pitfall is a fixed-length window that spans a recurring cycle unevenly, so seasonality, a weekly pattern smoothed with a 5-day window, for example, leaks into the smoothed line instead of being removed by it; the window should match or exceed the length of the seasonal cycle.