Table 7.

Mathematical model of the nine loss functions used.

Name of Loss Function	Abbreviation	Equation
root relative squared error	rrse	$\sqrt{\left[{\displaystyle {\displaystyle \sum }_{i=1}^n}{\left(x_i-y_i\right)}^2\right]/\left[{\displaystyle {\displaystyle \sum }_{i=1}^n}{\left(x_i-\tilde{x}\right)}^2\right]}$
symmetric mean absolute percent error	smape	$\frac{2}{n}{\displaystyle {\displaystyle \sum }_{i=1}^n}\frac{\left|x_i-y_i\right|}{\left|x_i\right|+\left|y_i\right|}$
mean absolute error	mae	$\frac{1}{n}{\displaystyle {\displaystyle \sum }_{i=1}^n}\left|x_i-y_i\right|$
mean squared error	mse	$\frac{1}{n}{\displaystyle {\displaystyle \sum }_{i=1}^n}{\left(x_i-y_i\right)}^2$
root mean squared error	rmse	$\sqrt{\frac{1}{n}{\displaystyle {\displaystyle \sum }_{i=1}^n}{\left(x_i-y_i\right)}^2}$
mean squared log error	msle	$\frac{1}{n}{\displaystyle {\displaystyle \sum }_{i=1}^n}{\left(ln\left(1+x_i\right)-ln\left(1+y_i\right)\right)}^2$
relative absolute error	rae	$\left[{\displaystyle {\displaystyle \sum }_{i=1}^n}\left|x_i-y_i\right|\right]/\left[{\displaystyle {\displaystyle \sum }_{i=1}^n}\left|x_i-\tilde{x}\right|\right]$
relative squared error	rse	$\left[{\displaystyle {\displaystyle \sum }_{i=1}^n}{\left(x_i-y_i\right)}^2\right]/\left[{\displaystyle {\displaystyle \sum }_{i=1}^n}{\left(x_i-\tilde{x}\right)}^2\right]$
root mean squared log error	rmsle	$\sqrt{\frac{1}{n}{\displaystyle {\displaystyle \sum }_{i=1}^n}{\left(ln\left(1+x_i\right)-ln\left(1+y_i\right)\right)}^2}$