# Short-Term Traffic Flow Forecasting via Multi-Regime Modeling and Ensemble Learning
## 5 Experimental Analysis
### Analysis of Forecasting Results
#### 5.2.2 Forecasting Results Analysis  
In the study, a one-step forecasting task was carried out. The modeled traffic flow measures include flow rate, occupancy, and speed. Moreover, four forecasting models were implemented and compared, including ARIMA, Regression Tree (RT), Ensemble Regression Trees (ERT), and ensemble regression trees based on multi-regime modeling (ERT-MRM), developed in the study. As a typical kind of time series model, ARIMA has been successfully applied in various domains [7] because of its solid theoretical foundations and good ability to capture local trends in stationary time series. Meanwhile, it is commonly used as a baseline in traffic flow forecasting tasks. There are three parameters to be determined in the ARIMA model (i.e., the number of autoregressive terms, \(p\); the number of nonseasonal differences needed for stationarity, \(d\); and the number of lagged forecast errors in the forecasting equation, \(q\). In this paper, the three parameters were determined using the Akaike information criterion (AIC). That is, \(p\), \(d\), and \(q\) were chosen when the forecasting model has the lowest AIC. RT is another popular model for forecasting modeling. It has shown to be competitive in many applications while possessing a good interpretability [48]. In this study, it was implemented as a pruned regression tree in order to achieve a good generalization performance. ERT is an ensemble version of the RT model. As mentioned, ensemble learning can improve the accuracy and robustness of the forecasting system. To this end, we added ERT to the comparative list. The number of the considered trees in ERT was set as 100 in order to balance the accuracy and efficiency of the model. The three models mentioned above did not utilize a multi-regime strategy, and hence the regimes were not used as the representative features in modeling. Instead, the ERT-MRM developed in this paper was implemented using a multi-regime strategy, and its component trees were also set as 100 for a fair comparison.  
The performances of the implemented models on the traffic flow data sets at the four study stations are illustrated in Figure 6. As the figure shows, the ERT-MRM model achieved the best performance on each data set. The ARIMA and RT models show similar forecasting errors, which are both higher than that of the ERT and ERT-MRM models. This might be because the ensemble strategy introduced in the latter two models can take advantage of the strengths of the component tree forecaster to effectively improve the accuracy and robustness of the forecasting system. Moreover, it can be observed that the ERT-MRM model shows a more competitive performance than the ERT model, meaning the multi-regime strategy is capable of being utilized to improve the accuracy of forecasting models [32]. Taken together, for the ERT-MRM model, the RMSEs associated with the flow rate measure are less than 14 veh/5-min, and the MAPEs are no more than 4%; the RMSEs associated with the occupancy measure are less than 0.01%, and the MAPEs are no more than 4.5%; and the RMSEs associated with the speed measure are less than 2 mi/h, and the MAPEs are no more than 1.5%.  
Figure 7 gives the comparisons between the observed and forecasted values of one-day traffic flow randomly selected from the test data set. From the figure, we can see that ERT-MRM can provide reliable traffic flow forecasts at all of the four stations. As a result, the model developed in this study can be perfectly used in proactive freeway management and control.  
Figure 6: Performance of the comparative forecasting models associated with different stations.  
Figure 7: _Cont_.