# An EMD-SARIMA-Based Modeling Approach for Air Traffic Forecasting
## 2 Literature Review
### On Single Theory-Based Forecasting Models  
Single theory-based forecasting models have experienced a development process from a statistics-based model stage to an AI-based model stage. The traditional time series models are statistics based models, and the famous work done by [PERSON] and [PERSON] [PERSON] and [PERSON] (1975) has built the fundamental basis of almost all related works in this area; later on, the relatively sophisticated Holt-Winters forecasting procedure has been proposed by [PERSON] (1999). For those forecasting models which have been put into the transportation industry in an early stage, the ARIMA-based time series model is the most representative one to predict the traffic volume, and the performance analysis has shown that the use of a subset of the ARIMA model can help to enhance the accuracy of short-term forecast results [PERSON] (1999); based on ARIMA, a Kohonen self-organized map-aided ARIMA, with the name KARIMA, was then proposed by [PERSON] et al. [PERSON] et al. (2006). It has broken the ARIMA model into two stages, by firstly clustering the time series samples and aggregating them using the Kohonen map, and then building the ARIMA model upon those clusters. The KARIMA model has shown improvement over the ARIMA based model; moreover, [PERSON] and [PERSON] [PERSON] and [PERSON] (2006); [PERSON] and [PERSON] (2006) have proposed two different models, which have been called vector ARMA (VARMA) and space-time ARIMA (STARIMA). Both of these two models have been applied in traffic flow forecasting. VARMA has employed parameter matrices to model dependence relations among different time series so as to capture a linear relationship between time series, whereas STARIMA has been proved to be more suitable for dealing with the situation where only fewer parameters are available in large-scale short-term traffic flow forecasting when compared with the ARIMA and VARMA models. The SARIMA model has been proposed by [PERSON] et al. [PERSON] et al. (2007) to try to capture the periodical features of the traffic flow on urban freeways.  
The AI-based models have mostly been proposed during the past 20 years. [PERSON] and [PERSON] [PERSON] and [PERSON] (1999) happened to be a group of researchers who applied an artificial neural network (ANN) in a short-term traffic flow forecast at the earliest stage of related research. With the development of various types of AI, the applicability of an ANN for short-term forecasting has then been questioned by [PERSON] et al. [PERSON] et al. (2000), who have pointed out that a neural network in a forecasting process can be seen as a \"black box\" with a hidden structure that cannot be approached easily and deeply by model builders. Apart from an ANN, many other AI-based theories have also been employed in short-term forecast model building. [PERSON] et al. [PERSON] et al. (2007) have proposed a support vector machine (SVM)-based short-term traffic flow prediction model, whereas [PERSON] et al. [PERSON] et al. (2009) have developed an online short-term traffic flow prediction tool based on an SVM and have investigated its performance in both typical and atypical traffic conditions. Fuzzy logic has also been employed in short-term forecast modeling by [PERSON] and Ye [PERSON] and [PERSON] (2010), and so has the Kalman filter theory, which has been employed in estimating real-time freeway traffic conditions by [PERSON] and [PERSON] and [PERSON] (2006).