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The mathematical models for traffic flow have been widely investigated for a lot of application, like planning transportation and easing traffic pressure by using statistics and machine learning methods. However, there remains a lot of challenging problems for various reasons. In this research, we mainly focused on three issues: (a) the data of traffic flow are nonnegative, and hereby, finding a proper probability distribution is essential; (b) the complex stochastic property of the traffic flow leads to the nonstationary variance, i.e., heteroscedasticity; and (c) the multistep-ahead prediction of the traffic flow is often of poor performance. To this end, we developed a Gamma distribution-based time series (GaTS) model. First, we transformed the original traffic flow observations into nonnegative real-valued data by using the Box-Cox transformation. Then, by specifying the generalized linear model with the Gamma distribution, the mean and variance of the distribution are regressed by the past data and homochronous terms, respectively. A Bayesian information criterion is used to select the proper Box-Cox transformation coefficients and the optimal model structures. Finally, the proposed model is applied to the urban traffic flow data achieved from Dalian city in China. The results show that the proposed GaTS has an excellent prediction performance and can represent the nonstationary stochastic property well.

Multistep-Ahead Prediction of Urban Traffic Flow Using GaTS Model