Question

select is calculated by squaring the individual forecast errors and then averaging the results over all t periods of data in the time series

Explanation:

To solve this, we recall the formula for the Mean Squared Error (MSE) in time series forecasting (or in general forecasting). The Mean Squared Error is calculated by first finding the forecast error for each period (which is the actual value minus the forecasted value), squaring each of these errors, and then taking the average of these squared errors over all the periods \( T \) in the time series.

Mathematically, if \( e_t = y_t - \hat{y}_t \) (where \( y_t \) is the actual value at time \( t \) and \( \hat{y}_t \) is the forecasted value at time \( t \)), then the Mean Squared Error (MSE) is given by:

\[
\text{MSE} = \frac{1}{T} \sum_{t = 1}^{T} e_t^2=\frac{1}{T} \sum_{t = 1}^{T} (y_t - \hat{y}_t)^2
\]

So the term that is calculated by squaring the individual forecast errors and then averaging the results over all \( T \) periods of data in the time series is the Mean Squared Error (MSE).

Answer:

Mean Squared Error (MSE)