Exponential Smoothing

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Calculate

Example: the same monthly sales of a shop. With α = 0.3, what is the sales forecast for next month? Change the series and α to work out your own case.

Series x_t In time order, separated by spaces or commas. Smoothing α

Step by step

What each term means

Smoothed Value (Sₜ): The estimate of the series' level at period t, and the forecast for t + 1.
Smoothing Constant (α): Between 0 and 1: how much weight to give the new observation. A high α reacts fast and copies the noise; a low α is stable and slow to notice changes.
Current Observation (xₜ): The value that has just arrived.
Weight of the Past (1 − α): The weight the previous smoothed value keeps. Since it already blends the earlier ones, each old observation loses weight in a geometric progression.
Previous Smoothed Value (Sₜ₋₁): The summary of the whole series up to the previous period. It is the method's memory: a single calculation per period, without storing the whole series.