## 6 Discussion
### Discussion: RNNs vs. Other Prediction Models  
With the increasing popularity, we first discuss the comparison between RNNs and statistical models, focusing on the comparison between RNNs and the representative work of statistical learning models, ARIMA. The ARIMA model is relatively simple, easy to understand and implement, and has low requirements for data preprocessing. Initially, ARIMA models were used for short-term traffic flow predictions, often restricted to a single arterial roadway or a small subset of an urban network. ARIMA models can provide reliable predictions in scenarios where the data are stable and the linear relationship is apparent. However, there are significant drawbacks, especially when dealing with complex, non-stationary time series data. ARIMA models typically assume that the data are stationary, which limits their ability to predict traffic during more complicated conditions, like peak traffic periods. Their ability to handle non-stationary data is limited. Although non-stationarity can be addressed through methods, such as differencing, traditional statistical models, typically do not perform as well as deep learning models when dealing with non-stationary data with complex seasonal and trend patterns. [PERSON] et al. (2014) evaluated the performance of LSTMs against statistical learning models in traffic flow prediction. The study indicates that integrating LSTMs with other neural network architectures shows better predictive results than ARIMA. Compared to the ARIMA model, LSTMs are more suitable for complex and dynamic traffic flow predictions, enabling better capture of key traffic flow characteristics. This is mainly attributed to LSTM's ability to model data with non-stationary patterns without pre-differencing or transformations effectively. Additionally, the structure of LSTMs allows them to learn from relatively complex data patterns, which is advantageous when dealing with the multidimensional nature of traffic systems, including spatial interactions and temporal dynamics. It is worth mentioning that RNNs and their variants naturally support multivariate input, making it easy to handle traffic data from multiple sites or road segments. In contrast, the ARIMA model is designed for univariate time series, dealing with autoregression, differencing, and moving averages of a single time series. Therefore, the ARIMA model used to forecast traffic flow predicts the flow for a single measurement point or road segment. In comparison, RNNs and their variants, like LSTMs and GRUs, can naturally handle inputs from multiple data sources and effectively capture the temporal dependencies and interaction effects among these variables. This makes them perform better in applications, such as traffic flow prediction, where analyzing and forecasting dynamic interactions across multiple points are required. Next, we discuss the comparison between RNNs and traditional machine learning models. Firstly, regarding handling time series data, K-NN and SVR are not specifically designed for sequence prediction. They often require complex feature engineering to include time information, such as creating time window features or lag features. While these models perform well on non-time series data, like classification and regression problems, they are less intuitive or efficient than RNNs in native time series processing. When dealing with multivariate and spatial relationships, RNNs support multivariate input, enabling the simultaneous prediction of data from multiple traffic monitoring points. Although RNNs do not directly handle spatial data, incorporating techniques, like CNN layers or attention mechanisms, allows for effective learning of spatial relationships between points in the traffic network. In traditional machine learning, models like K-NN and SVR can handle multivariate problems but often lack built-in mechanisms for handling spatial or temporal dependencies. They are not very efficient when dealing with data from multiple monitoring points.