What is the mathematical formula for exponential smoothing?

Conditions

• Requires an initial forecast value.
• Alpha must be between 0 and 1.

Reasoning, step by step

1. Identify the previous forecast $F(t-1)$.
2. Identify the previous actual value $A(t-1)$.
3. Calculate the previous forecast error: $A(t-1) - F(t-1)$.
4. Multiply the error by the smoothing constant alpha.
5. Add this product to the previous forecast to get $F(t)$.

Example

The text overlay displays the equation $F(t) = F(t-1) + \alpha \cdot (A(t-1) - F(t-1))$. The Excel formula bar shows =C4+$B$$4*(B4-C4)$, which corresponds to this mathematical definition.

Common misconceptions

• Using the current actual value $A(t)$ in the error term instead of the previous actual $A(t-1)$.
• Thinking alpha is added to the forecast rather than multiplying the error term.

Watch the explanation

Explore next

• How do I implement the exponential smoothing formula in Excel?
• What does the smoothing constant alpha control?
• How is the initial forecast determined?