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>