# Short-Term Traffic Flow Forecasting via Multi-Regime Modeling and Ensemble Learning
## 2 Literature Review  
During the past decades, researchers have explored and developed a vast number of traffic flow forecasting models. As traffic flow is recorded as a time series format, which can be effectively described and modeled by typical time series models, autoregressive integrated moving average (ARIMA) was applied by [PERSON] and [PERSON] [7] to establish a short-term traffic flow forecasting model. The model can accurately capture the local trends in traffic flow. Nevertheless, given the cyclical characteristic of traffic flow, the first difference of a traffic flow time series will not produce a stationary series, leading to inaccurate forecasts. In view of this, a seasonal autoregressive integrated moving average (SARIMA) model was developed by [PERSON] et al. [8] to forecast urban freeway traffic flow. The results indicated that the SARIMA models outperform the nonparametric regression (NPR), artificial neural network (ANN), and historical average models. [PERSON] et al. [9] designed a multistep forecaster based on a SARIMA model and an embedded adaptive Kalman filter model. The advantage of the designed model is that it is easy to implement and is computationally inexpensive. Kalman filtering is another efficient model, which uses the state of the previous moment to compute the best estimate of the state at the current moment. Some researchers extended the Kalman filtering to forecast short-term traffic volume [10; 11]. The ARIMA, SARIMA, and Kalman filter models are capable of accurately and timely forecasting stable traffic flow, while neither is able to capture the nonlinear patterns in traffic flow. To effectively capture the nonlinear patterns in traffic flow, a series of more elegant models were proposed. The NPR models [12; 13] were presented to avoid the shortcomings of the parametric models (e.g., ARIMA and SARIMA) and to make more accurate forecasts in non-stationary traffic flow. The main advantages of the NPR models are that they do not need to make priori assumptions,and have a high flexibility and intuitive expression [14]. It should be noted that the NPR models are sensitive to outliers usually underlying in traffic flow data. Recently, SVR has drawn increasing attention, and been successfully applied in short-term traffic forecasting [15; 16]. It needs to be indicated that the standard SVR model requires a blind and time-consuming searching procedure to find suitable hyperparameters. To improve the computational efficiency, some more advanced SVRs have been presented [17; 18]. Because of the capability to capture the uncertainty and nonlinearity in traffic flow, the ANN models were designed for short-term traffic flow forecasting tasks. Although each neuron in ANN has a very simple function, the network, composed of a large number of neurons, can possess significantly powerful functions [19; 20]. In the past decade, deep learning models, in particular deep neural networks (DNN), have achieved great success in various domains. Accordingly, several researchers presented a number of traffic flow forecasting models based on DNN. [PERSON] et al. [21] put forward a deep architecture model using autoencoders as building blocks to represent traffic flow features. Experimental results demonstrated the superiority of the DNN model. [PERSON] and [PERSON] [22] showed that deep learning architectures are able to capture the nonlinear spatiotemporal effects resulting from the transitions between free flow, breakdown, recovery, and congestion in traffic flow. More recently, [PERSON] et al. [23] introduced the spatial and temporal attentions that are utilized to capture the spatial dependencies between road segments and temporal dependencies between time steps into the DNN model. While the models mentioned above have been proven to be effective in short-term traffic flow forecasting, an issue that cannot be ignored is that the work mechanisms of the models have not been easily understood by decision-makers. That is, the forecasting results lack a convincing interpretation.