Why are there two different formulas for exponential smoothing and which one should I use?

There are two mathematically equivalent forms of the exponential smoothing formula. The first is the error correction form:

F_{t+1} = F_t + \alpha(A_t - F_t)

. The second is the weighted average form:

F_{t+1} = \alpha A_t + (1 - \alpha)F_t

. The video recommends using the weighted average form because it is computationally easier for manual calculations.

Conditions

You are performing exponential smoothing calculations.
You want to understand the relationship between the two formula forms.

Reasoning, step by step

Recognize the error correction form: $F_{t+1} = F_t + \alpha(A_t - F_t)$ .
Distribute $\alpha$ into the parentheses: $F_{t+1} = F_t + \alpha A_t - \alpha F_t$ .
Group the $F_t$ terms: $F_{t+1} = \alpha A_t + F_t - \alpha F_t$ .
Factor out $F_t$ : $F_{t+1} = \alpha A_t + (1 - \alpha)F_t$ .
Conclude that both formulas yield the same result, but the weighted average form is simpler to calculate.

Example

The video shows a double-headed arrow connecting the two formula boxes and states, "Note that both formulas will give the same result, it is just a little easier to use the second one."

Common misconceptions

Believing that the two formulas produce different results.
Using the error correction form for manual calculations, which can be more prone to arithmetic errors.

Watch the explanation

YouTubeForecasting: Exponential Smoothing, MSE

1:03 – 1:29Watch this moment ↗

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Answers are generated from source material and independently checked. Consult the original video or creator if something is unclear.