11.3 Moving averages

A moving average smooths short-term variation by averaging the most recent observations. For a window of size \(k\),

\[ \widehat{y}_{t+1}=\frac{1}{k}\sum_{i=0}^{k-1}y_{t-i}. \]

Moving averages are easy to explain and useful as baselines. A short window responds quickly but can be noisy. A long window is stable but reacts slowly to change. A simple moving average does not represent trend or seasonality unless those features are addressed separately.