12.2 Performance Measurements
12.2.1 Error terms
- Mean error (ME):
\[\begin{equation} ME=\frac{1}{n}\sum_{ }^{ }\left(Y_t-\hat{Y}_t\right)$ \tag{12.15} \end{equation}\]
- Mean Absolute Deviation (error):
\[\begin{equation} MAD\left(i.e.\ MAE\right)\ =\ \frac{1}{n}\cdot\sum_{ }^{ }\left|Y_t-\hat{Y}_t\right| \tag{12.16} \end{equation}\]
- Mean Percentage Error (MPE):
\[\begin{equation} MPE\ =\ \frac{1}{n}\ \sum_{ }^{ }\frac{\left(Y_t-\hat{Y}_t\right)}{Y_t} \tag{12.17} \end{equation}\]
- Mean Absolute Percentage Error (MAPE):
\[\begin{equation} MAPE\ =\ \frac{1}{n}\ \sum_{ }^{ }\frac{|\left(Y_t-\hat{Y}_t\right)|}{|Y_t|} \tag{12.18} \end{equation}\]
- Mean-Squared Error (MSE):
\[\begin{equation} MSE=\frac{1}{n}\sum_{ }^{ }(Y_t-\hat{Y}_t)^2 \tag{12.19} \end{equation}\]
- Root Mean-Squared Error:
\[\begin{equation} RMSE=\sqrt{MSE} \tag{12.19} \end{equation}\]
12.2.2 Multicollinearity
VIF
\[\begin{equation} VIF_j=\frac{1}{1-R_j^2} \tag{5.7} \end{equation}\]
Where \(j = 1,...,k\)
Thus, we see that Rsquare is obtained from regression each IDV against the remaining variables. We can then have the following outputs:
- VIF = 1, no milticollinearity
- VIF > 10, indicates multicollinearity
If one gets an indication of multicollinearity, then one should drop one of the correlated variables.