Long-Range Dependence and Multifractality of Ship Flow Sequences in Container Ports: A Comparison of Shanghai, Singapore, and Rotterdam

The prediction of ship traffic flow is an important fundamental preparation for layout and design of ports as well as management of ship navigation. However, until now, the temporal characteristics and accurate prediction of ship flow sequence in port are rarely studied. Therefore, in this study, we investigated the presence of long-range dependence in container ship flow sequences using the Multifractal Detrended Fluctuation Analysis (MF-DFA). We considered three representative container ports in the world—including Shanghai, Singapore, and Rotterdam container ports—as the study sample, from 1 January 2013 to 31 December 2017. Empirical results suggested that the ship flow sequences are deviated from normal distribution, and the sequences with different time scales exhibited varying degrees of long-range dependence. Furthermore, the ship flow sequences possessed a multifractal nature, where the larger the time scale of ship flow time series, the stronger the multifractal characteristics are. The weekly ship flow sequence in the port of Singapore owned the highest degree of multifractality. Furthermore, the multifractality presented in the ship flow sequences of container ports are due to the correlation properties as well as the probability density function of the ship flow sequences. The study outlines the importance of adopting these features for an accurate modeling and prediction for maritime ship flow series.