5.6 Forecast accuracy

• Quality of the applied forecasting method is evaluated with different measures based on the forecast errors

• Forecast error \(e_t\) is the difference between actual value \(Y_t\) and the forecast value \(F_t\)

\[\begin{equation} e_t=Y_t-F_t~~~~t=1,2,...,T \tag{5.3} \end{equation}\]

• Forecast value \(F_t\) is usually obtained using past actual values \(Y_{t-1}\), \(Y_{t-2}\),…,\(Y_1\)

\[\begin{align} F_t=&f(Y_{t-1},~Y_{t-2},...,Y_{1}) \\ \\ Y_t=&f(Y_{t-1},~Y_{t-2},...,Y_{1})+e_t \\ \tag{5.4} \end{align}\]

• Most commonly used forecast accuracy measures are:

1. Mean erorr

\[\begin{equation} ME=\sum_{t=1}^T e_t \tag{5.5} \end{equation}\]

2. Mean absoulte erorr

3. Mean squared erorr

4. Root mean squared error/span>