# Evaluating Prediction Models for Airport Passenger Throughput Using a Hybrid Method
## 4 Evaluation Results and Discussion
### The Evaluation Results
#### 4.1.1 Time Series Models  
For the trend extrapolation models including linear trend, quadratic trend, cubic trend, power trend, exponential trend and logarithmic trend models, the most effective model is firstly determined for a certain airport. The coefficient of determination is used to judge the effectiveness of the models and the model with the largest coefficient of determination is selected as the model for prediction. If the coefficients of determination of all the six models are smaller than 0.8, the trend extrapolation models are deemed to be failed for prediction. For the exponential smoothing models including quadratic exponential smoothing models and cubic exponential smoothing models, different values of the smoothing coefficients exert a tremendous influence on the predicted results. The most effective exponential smoothing model is determined by computing the MAPE of models under different smoothing coefficients. By setting the MAPE as 10%, the distribution of the number of most effective exponential smoothing models for airports under different smoothing coefficients is shown in Figure 3. For quadratic exponential smoothing models, when the smoothing coefficient is set as 0.45, the corresponding model is suitable for most airports under the given error. When the smoothing coefficient is set as 0.2, the corresponding cubic exponential smoothing model is suitable for most airports under the given error. For the grey models, at least four points are needed to initiate the model which means that the minimum order number of a GM (1,1) is 4. By accumulating the observation sequences, the models are established and the effectiveness of the models is judged by the relative error test, correlation test and posterior difference test. The evaluating results of the above models are shown in Table 2, from which we can see that the exponential smoothing models perform better than the other two types of models. The exponential smoothing models can be used as good models for 68% of all the 203 airports under all four evaluating criteria. The trend extrapolation models show better performances in larger airports. The grey models can predict accurately for fewer airports because only a few airports show the characteristics of exponential growth. The applicability of the models on different levels of airports is shown in Table 3. The time series models are defined to be effective for an airport when at least one of the models is a good model under the given criterion. For the airports with APT of more than 10 million, 100% of the airports can be predicted effectively. Meanwhile, the time series models show poor applicability to airports with APT of less than 2 million. The criteria do not perform much influence on the predicted results. Considering the unavailability of the time series models, the airports with APT between 2 million and 10 million are studied in detail. There are only three airports that cannot be predicted by the time series models, which are shown in Figure 4. The Yangzhou airport (YTY) started running in 2012 and the little data make the models difficult to fit the observations well. The Yichang airport (YIH) is influenced by the Three Gorges Dam Project and its APT has shown explosive growth since 2014 when the Three Gorges Dam Project was opened to the public. The Zhangjiajie airport (DYG) develops depending much on the tourist industry. At first, the Zhangjiajie airport experienced a rapid expansion owing to the development of tourism resources. Then for a while, the Zhangjiajie airport was affected by the development of the high-speed railway. In 2017, after the vis on arrival was permitted, the APT of the airport returned to positive growth. For the airports with APT less than 2 million, 49 airports cannot be predicted by the time series models. Eighteen airports lack sufficient data. Eight airports suffer from data interruption because of expansion or relocation. The others are driven by external forces and show a lot of uncertainties like the Jiuzhaigou (JZH) airport.