*2.4. Performance Indicators of Forecasting Models*

In terms of accuracy evaluation of water demand forecasting models, variety of measures are available to characterize the performance of the models [1,7,9]. This study adopts four widely used indicators as evaluation criteria, including the mean absolute error (MAE), the mean absolute percentage error (MAPE), the root means square error (RMSE), and the coefficient of determination (*R*2). The equations of these aforementioned indicators are shown as follows:

$$\text{MAE} = \frac{1}{N\_f} \sum\_{i=1}^{N\_f} |y\_i - \hat{y}\_i| \tag{11}$$

$$\text{MAPE} = \frac{1}{N\_f} \sum\_{i=1}^{N\_f} \frac{|y\_i - \hat{y}\_i|}{y\_i} \times 100\% \tag{12}$$

$$\text{RMSE} = \sqrt{\frac{1}{N\_f} \sum\_{i=1}^{N\_f} (y\_i - \hat{y}\_i)^2} \tag{13}$$

$$R^2 = 1 - \frac{\sum\_{i=1}^{N\_f} (y\_i - \hat{y}\_i)^2}{\sum\_{i=1}^{N\_f} (y\_i - \overline{y})^2} \tag{14}$$

where *yi* and *y*ˆ*<sup>i</sup>* are the observed value and the predicted value of water demand at time *i*, respectively; *y* and *y*ˆ are the corresponding mean values; *Nf* is the number of forecasted time steps, which is equal to 96 for the water demand forecasting problem with a one day horizon and a frequency of 15 min.
