How does a moving average filter work in time series smoothing?
Instruction: Describe the process of applying a moving average filter to time series data and its effect.
Updated
Official answer
A moving average smooths a series by averaging nearby observations. For a trailing window of width k at time t, average the observations from t−k+1 through t. This uses only information available by t, assuming those observations have arrived.
For values 2, 4, 6, 10, a full three-observation trailing average is undefined for the first two positions, then equals 4 and 20/3 (about 6.67). If partial windows are allowed instead, document their changing denominators; do not silently treat missing observations as zero.
A centered average uses observations on both sides of a time point. It can help retrospective trend estimation, but those future observations are unavailable for an online feature at that time. Centering does not remove the information boundary.
Longer windows suppress more short-term variation but can blur turning points and meaningful events. A trailing filter introduces delay, and smoothing does not reveal a guaranteed “true” trend. Choose the window from the task and validate downstream decisions on later data.
For irregular or missing timestamps, distinguish a fixed count of observations from a fixed calendar duration. A seven-row window is not necessarily seven days. This smoothing operation is also distinct from the moving-average error model in ARMA notation.