How do you calculate the Mean Squared Error (MSE) for exponential smoothing forecasts?

Conditions

• You have calculated the forecasts for each period.
• You have the actual sales data for each period.
• Errors are not calculated for the first period if $F_1 = A_1$.

Reasoning, step by step

1. Calculate the forecast error for each period: $E_t = A_t - F_t$.
2. Square each forecast error: $E_t^2$.
3. Sum all the squared errors.
4. Divide the sum of squared errors by the number of periods with errors ($n$).

Example

In the video, the errors for weeks 2 through 7 are calculated, squared, and summed. The sum of the squared errors is then divided by 6 (the number of periods with errors) to obtain an MSE of 11.58.

Common misconceptions

• Taking the square root of the average of the squared errors (which would be RMSE, not MSE).
• Including the first period's error in the calculation if $F_1 = A_1$.
• Dividing by the total number of periods instead of the number of periods with errors.

Watch the explanation

Explore next

• Why is there no forecast error calculated for the first week in exponential smoothing?
• How do you calculate the next forecast in exponential smoothing with a smoothing constant of 0.2?