Table 2 Mathematical equations used to calculate statistical validation metrics
Metrics | Equations | |
|---|---|---|
MAE | Mean absolute error | \(\frac{1}{x}\sum\limits_{i=1}^{x}|({a}^{i}-{b}^{i})|\) |
MSE | Mean square error | \(\frac{1}{x}\sum\limits_{i=1}^{x}|{({a}^{i}-{b}^{i})}^{2}|\) |
RMSE | Root mean square error | \(\sqrt{\frac{1}{x}\sum\limits_{i=1}^{x}{({a}^{i}-{b}^{i})}^{2}}\) |
RSE | Relative Squared Error | \(\frac{\sum_{i=1}^{x}{({b}^{i}-{a}^{i})}^{2}}{\sum_{i=1}^{x}{({b}^{i}-\overline{b })}^{2}}\) |
MAPE | Mean absolute percentage error | \(\frac{100\%}{x}\sum\limits_{i=1}^{x}(|\frac{{a}^{i}-{b}^{i}}{{b}^{i}}|)\) |
SMAPE | Symmetric Mean Absolute Percentage Error | \(\frac{100\%}{x}\sum\limits_{i=1}^{x}(|\frac{{\widehat{|a}}_{i}-{b}^{i}|}{{\widehat{|a}}_{i}\left|+{|b}^{i}\right|/2}|)\) |
MASE | Mean absolute scaled error | \(\frac{1}{x}\sum\limits_{i=1}^{x}\frac{|{a}^{i}-{b}^{i}|}{\frac{1}{n-1}\sum_{i=2}^{x}|{a}^{i}-{b}^{i}|}\) |