## 3 Results  
After the previous calibration phase, in which all parameters, coefficients and weights of the network were estimated, it is possible to input into the hybrid model the noise emissions of previous periods and the forecasting errors generated by the DD-TSA model: in this way, it is possible to have, as the output, the predictions of \(\mathrm{L_{Aeq,16\;h}}\) for future days. In the performance test phase, the \(\mathrm{L_{Aeq,16\;h}}\), and the errors generated during DD-TSA forecasts from period 1101 to 1200 (15 May 2010 to 22 August 2010) were used. As stated before, these data were not used to calibrate the coefficients and parameters of the DD-TSA model or to update the weights of the ANN, so they constitute an effective dataset to evaluate the real predictive power of the developed hybrid model. In this article, the authors have adopted two error metrics: mean percentage error (MPE) and the Coefficient of Variation of the Error (CVE). Once the three models (DD-TSA, DD+ANN (\(t\)-1) and DD+ANN (\(t\)-7)) have been calibrated, a detailed comparison can be pursued. In this section, the comparison is performed qualitatively, with a plot of the model predictions and of the actual values, and quantitatively using residual distributions analysis and error metrics (MPE and CVE). Figure 9 reports the actual and predicted time series in two different intervals of the entire range under study. All the models follow the general slope of the data, with moderate agreement. Figure 8: Regression fitting of the ANN (\(t\)-7) model after the network simulation on the calibration data. The plot is relative to the second tuning. As for the quantitative comparison, the \"overall\" residuals of the models can be evaluated by looking at the difference between observed and predicted values. In particular, for the DD-TSA model, \(e_{t}^{*}\) is computed as in Formula (3), whereas the hybrid models are computed as in Formula (5). In Table 10, the statistics of the residuals of all the models are presented. The mean value of the residuals is basically negligible for all three models. The two hybrid models exhibit a lower standard deviation compared to the DD-TSA model, suggesting a lower dispersion of the error. Residual autocorrelation has been tested with an autocorrelation plot (Figure 10). A very high correlation is detected in the DD-TSA residuals dataset. This means a lot of information in this series is present that the neural network can use to improve the prediction. Looking at the hybrid models, both exhibit a much lower autocorrelation compared to the DD-TSA model, for any value of lag. In particular, the DD+ANN (\(t\)-1) model seems to be able to better explain the variance in the data, since it quite completely removes the autocorrelation in the residuals. On the contrary, the residuals dataset of the DD+ANN (\(t\)-7) still shows a non-negligible autocorrelation, especially for values of the lag up to 6. This was expected since this model uses the 6 closer data to provide the forecast. In Table 11, the values of the autocorrelation function computed for 7- and 14-day lags are presented. It is easy to notice the very low level of autocorrelation in the residuals dataset of the two hybrid models. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & **Mean** & **Std. Dev.** & **Median** & \multirow{2}{*}{**Skew**} & **Kurt** \\  & **[dBA]** & **[dBA]** & **[dBA]** & & \\ \hline DD-TSA & 0.01 & 0.90 & 0.15 & \(-\)0.58 & \(-\)0.01 \\ DD+ANN (\(t\)-1) & \(-\)0.02 & 0.52 & \(-\)0.04 & \(-\)0.13 & 2.73 \\ DD+ANN (\(t\)-7) & 0.01 & 0.63 & 0.02 & \(-\)0.34 & 4.13 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Residual statistics resume for the 1087 comparison \(\text{Leq}_{16\text{ h}}\) in the calibration phase. Figure 9: Time history comparison between real data DD-TSA, DD+ANN (\(t\)-1) and DD+ANN (\(t\)-7) predictions. In (**a**), data are shown from 26 November 2007 to 5 May 2008. In (**b**), the period between 26 October 2009 and 3 February 2010 is reported.