## 4 Conclusions
In particular, the model DD-TSA, characterized by the largest forecast horizon, shows a higher error in the predictive phase. It is noteworthy to consider that, in the calibration phase, all the available data were considered and used, even if a sudden drop in the mean level, interrupting the stationarity of the time series, was present. In this way, the authors performed a \"non-informative\" calibration of the model itself, which resulted in very good provisional properties. Even if such a sudden drop in the noise level was due to malfunctioning or accidental events, the hybrid model preserves its good provisional capability when calibrated with those data. A substantial improvement in the error statistics, normality and autocorrelation is obtained with the two hybrid models, even though this new technique is characterized by a short forecast horizon. The forecast errors provided by the hybrid models, with respect to the ones obtained with the DD-TSA model, show a lower mean value (but a slightly higher standard deviation), a normal distribution and, in the case of the DD+ANN (_t_-7) model, a lower autocorrelation for the 7 and 14 lags. The limitations of this study are mainly related to the need for a large and non-biased dataset to calibrate the models, to tune the hyperparameters and the parameters of the selected approach and to provide reliable forecasts. The strength of such models, in fact, is that they use input only past measurements of the acoustic descriptor to be predicted, in our case, the daily L\({}_{\text{Aeq,16 h}}\). It does not require any information about traffic flows, traffic composition, average speed, etc., as the standard Road Traffic Noise Models (RTNMs). Of course, this makes the model very sensible to the quality of the input data. From a practical point of view, the authors do not believe this model could be easily and directly used for the commonly used procedure for strategic noise mapping of an urban area. The amount of data required for such a procedure, in fact, does not match with the essential nature of the here presented model, which deals with one single input. On the other hand, our model can be useful to validate any kind of mitigation actions designed and predicted with the very same tools involved in the noise mapping procedures. Any time a strong action on the traffic road framework is implemented, in fact, a new acoustic scenario is born. While its prediction requires many different types of data and a more complex computational framework, the acoustic changes deriving from it could be included in the model with a new calibration, which would certainly modify the model parameters values and adapt to the new conditions. This feature highlights how the model is suitable to be used wherever an unattended long-term measurement station is installed since this kind of instrument provides a time series of noise levels that are perfect for the model calibration. The availability of continuous measurements, in fact, allows for the performance of new calibrations when the model results start to deviate from the observed data. Another limitation of the hybrid models is the short forecast range, compared to the DD-TSA model. The \"one step ahead\" prediction made with the DD+ANN (_t_-1) model appears to be more precise but may be too short for urban planning purposes. The DD+ANN (_t_-7) model seems to be the best compromise, offering a one-week prediction range with a low predictive error. Future steps of this research will be the calculation of the trend of the time series considering only a short time interval, not far from the periods in which the forecast is computed, in order to avoid the effect of strong changes in the series mean. In addition, a further evolution of this technique can be the construction of a new hybrid model using a preliminary ARIMA linear model followed in cascade by a recurrent neural network (for instance Hopfield network).