Exponential Smoothing (Alpha One-Half)

Computing ETS(1/2) by hand on a pinned integer series — recursive half-and-half blending gives exact dyadic fractions at every step.

highlighted = computed this step

Exponential smoothing matrix

Exponential smoothing initialises with the first value and recursively blends each new observation into the running estimate using equal split between new and old.

\text{exponential smoothing}

Raw series (dot plot)

The raw series as dots. The smoothed values follow the input, weighting recent observations more heavily than older ones.

\text{raw series}