Smoothing Is Not Forecasting - Time Series Mechanics

Pinning the smoothing arithmetic exactly proves how the smoother is computed — and demonstrates precisely why that says nothing about predictive accuracy.

highlighted = computed this step

Naive forecast: last smoothed value carried forward

The smoothing formula gives exact values for every observed period. Carrying the last smoothed value forward into the next period is the naive forecast. This uses the smoothing arithmetic only — it says nothing about future accuracy.

\text{smoothing arithmetic}

Observed series with naive forecast dot

The observed series as dots, with the naive forecast as a single additional dot. The forecast is pinned by the formula, not validated against future data.

\text{observed series}