# Multi-Step Traffic Speed Prediction Based on Ensemble Learning on an Urban Road Network
## 2 Related Work  
In this section, a relevant background review about works on traffic speed prediction including parametric methods and non-parametric methods [8; 9], machine learning, and multi-step prediction is provided. Parametric methods, a well-structured family of models, estimate the model parameters based on the training data and have been widely used to conduct traffic forecast. For example, the auto-regressive integrated moving average (ARIMA) model was proposed in 1970s to predict short-term freeway traffic data [10]. Additionally, [PERSON] et al. [11] proposed a KARIMA prediction model to forecast traffic flow, which combined Kohonen maps with ARIMA time series. Then, [PERSON] et al. [12] provided a theoretical and empirical analysis of a seasonal ARIMA method, and [PERSON] et al. [13] extended it into the scenarios of the limited input data. In [PERSON]'s scheme, the prediction of the next day situation (24 h, start from the prediction moment) was only based on the historical data in the last three days. In 1984, [PERSON] et al. [14] applied Kalman filtering (KF) theory to traffic prediction and proved that KF could perform well in traffic prediction, and [PERSON] et al. [15] introduced the adaptive KF approach to forecast stochastic short-term traffic flow. Along this line, [PERSON] et al. [16] presented a KF model for travel speed prediction by minimizing the variance between the real-time speed measurement and its prediction. [PERSON] et al. [17] presented an intuitive formula to predict link travel time based on the degree of traffic congestion for route choice optimization. Unlike the parametric methods, non-parametric ones have ability to flexibly capture the stochastic and nonlinear features of traffic state (i.e., speed, flow, occupancy, travel time). [PERSON] et al. [8] pointed that traffic forecasting methods with computational intelligence (CI) have gradually replaced the traditional statistical ones, because they need no or little prior assumptions for input variables. As typical representatives, artificial neural networks (ANNs) have been successfully applied in many transportation domains [18; 19]. ANNs are mathematical models that formulate information processing systems by imitating the structure and function of the neural network of the brain. For example, [PERSON] et al. [20] proposed an advanced, genetic algorithm based multi-layered structural optimization strategy to predict traffic flow. Different from ANNs, [PERSON] et al. [21] proposed wavelet-based higher-order spatial-temporal (Wavelet-HST) method to accurately predict network-scale traffic speed with an improvement of 7.8%\(\sim\)10.5% in the root mean square error than other six benchmark methods. Moreover, [PERSON] et al. [22] improved the original KNN model based on spatiotemporal correlation for traffic prediction. In recent years, with the rapid development of machine learning and deep learning techniques, more and more ITS researchers have begun to adopt these kinds of techniques for high-accuracy traffic prediction. As pointed out by [PERSON] et al., the LSTM-NN can overcome the problem of back-propagated error decay by using memory blocks and has a better capability for time series prediction with long temporal dependency [23]. Additionally, a single-step support vector machine (SVM) with spatiotemporal parameters was proposed in 2017, which provided short-term traffic speed prediction results (5-min) with error ranging from 3.31% to 15.35% [24]. Moreover, [PERSON] et al. [25] developed an extreme gradient boosting (XGBOOST) model with wavelets decomposition and reconstruction to predict the short-term traffic flow, which outperformed SVM. Although single models are studied by many researchers and proved to be suitable for many cases, they still have some shortcomings [25]. Alternatively, it is a much better way to fuse the results from different prediction methods combined one to achieve better prediction accuracy than single predictor.