Exponential vs Moving Average - Time Series Mechanics

Two smoothers on the same series: MA(2) with equal window weights vs ETS(1/2) with geometric weights — same starting series, different values, different philosophy.

highlighted = computed this step

MA(2) vs exponential smoothing

Moving-average applies equal weights to a fixed window and discards older values. Exponential smoothing applies geometrically decaying weights to all past values.

\text{MA vs exponential}

Raw series (dot plot)

The raw series as dots. Equal-weight smoothing and geometric-weight smoothing diverge when recent values differ from the older average.

\text{raw series}