## 4 Analysis of Methods for Forecasting Transportation Flow
### Based on Mathematical and Statistical Models  
The model based on mathematical statistics applies the relationship between random variables for quantitative description, such as the time series method, grey models (GMs), Kalman filter (KF), etc. The time series method aims to establish the algorithm model based on the rule of the time series change in baggage flow, such as the autoregressive model, the autoregressive integrated moving average model (ARIMA), etc.  
Time Series Analysis (TSA) is a mathematical and statistical method used to analyze and predict changes in data based on their temporal order. It is widely used in various fields, including transportation. TSA elucidates data behavior by extracting information on trends, seasonality, and residuals from the data [34]. Based on this understanding, predictions and decisions are made. The main advantage of TSA lies in its transparent analysis process, in contrast to the \"black box\" phenomenon often associated with the analysis processes of artificial neural networks. ARIMA is the most common prediction model used for time series analysis. When modelling, the data need to be stabilized first. Since the baggage flow is periodic, the seasonal difference can be used to stabilize the baggage flow data. Then, ARIMA research, the SARIMA model, is used. [PERSON] employed the residual method to fit a SARIMA model, choosing the model with the smoothest residuals for predicting the passenger flow of a U.S. airline over the next 24 months. Based on this model, he concluded that the airline's passenger flow is expected to continue growing [35]. However, its disadvantage is that the time series data must be stable, so it lacks advantages in nonlinear analysis. TSA typically yields good results for long-term predictions of passenger or baggage flow, yet it proves less effective for short-term forecasts. For example, [PERSON] et al. used SARIMA to predict the traffic flow on freeways for a short time [36]. During this research, they found that the prediction accuracy of the regular traffic flow was high. However, the mean absolute percentage error (MAPE) of the prediction on the random traffic flow was more than 10%.  
The principle of the GM is that the modelling process of generating exponential law through the accumulation of baggage flow data or other ways has a good effect on short-term prediction. However, it is not ideal for solving multiclassification problems. For example, [PERSON] used the dynamic improved grey model to calculate the passenger throughput of China Hongqiao airport from 2008 to 2017 to predict the situation from 2018 to 2020 [37]. Although the relative error of the simulation was only 2.1%, the actual result had a significant deviation.  
The KF aims to calculate the optimal value of the current traffic based on the traffic at the previous and current time nodes and then calculate the next time node value. Its advantages are its nonlinear processing ability and accuracy, but it is easy to be disturbed by noise data. Meanwhile, the calculation amount is large because of the complex model. [PERSON] and [PERSON] et al. applied the KF to predict traffic flow; the prediction results were more accurate after eliminating the noise of the data, but the prediction effect on highly nonlinear problems was poor [38; 39].