Moving Average Lag - Time Series Mechanics

MA(2) on a series with a clear peak — the smoothed peak arrives one step after the raw peak, revealing the inherent lag of any moving average.

highlighted = computed this step

MA(2) matrix

The window-two average at each position uses that value and the one before it. The first position is undefined. The raw series peaks before the smoothed series — the smoother lags.

\text{MA matrix}

Raw series (dot plot)

The raw series as dots over time. The smoothed peak arrives one step after the raw peak.

\text{raw series}