## 1 Introduction  
The analysis of the time series characteristics of port ship flow sequences and the accurate prediction of port ship flow can provide references for the port layout design and the management of ship navigation. Port congestion has been recognized as a serious problem in all large ports in the world, which has a significant effect on the shipping date, the transportation cost, economic loss of the owner of the goods, and even the development of ports [1; 2]. Nevertheless, understanding the arrival laws and accurate prediction of the port ship traffic flow are two keys to solve this problem. Therefore, this paper aims to study the arrival laws of ship traffic flow in container ports based on the long-range correlation and multifractality, and then, to provide a reference and theoretical basis for effective modeling and prediction of port ship flows.  
There is an abundance of literature on long-range dependence for time series data, such as biomedical data [3; 4; 5], stock returns [6; 7; 8], hydrology [9; 10; 11], and climatology [12; 13; 14]. However, only a few studies focus on traffic flow sequences [15; 16] and the research on maritime traffic flow sequences are very limited. This is mainly due to the difficulty in obtaining data on port ship traffic flow in the maritime sector. However, in recent years,there are more and more relevant studies on the application of ship AIS data [17; 18]. This makes it possible to study the time series of maritime ship flow.  
Studies on maritime traffic flow, especially the ship flow sequences in the ports, are very important as they can provide basic decisions for the allocation of port operation infrastructures, rational port planning, and port investment. Furthermore, if the ship flow sequences in ports are long-range dependent and multifractal, then the traditional ships flow prediction models should revalue to incorporate this type of volatility. Unfortunately, there is no universally accepted theory to define the volatility of traffic flow sequence. In order to understand the irregular patterns of ship flow time series, especially for prediction, we need to know whether the maritime traffic flow system follows chaotic, random, or deterministic structural patterns. The complex pattern is the motivation behind the study of maritime ship flow series through the Multifractal Detrended Fluctuation Analysis (MF-DFA).  
The contributions of this study are threefold: First, we present a descriptive statistics of the ship traffic flow time series. Second, we analyze the long-range dependence correlation characteristics of the ship traffic flow series using the Hurst exponent. Third, we determine the degree of multifractality of the ship traffic flow of the different ports through the Multifractal Detrended Fluctuation Analysis, and compare them based on the MF-DFA results. Our results suggested that the ship flow sequences at different time scales in the ports of Shanghai, Singapore, and Rotterdam showed different degrees of long-range dependency. Therefore, the ship flow prediction models should incorporate the long-range dependency in forecasting. In addition, the results indicated that the ship flow sequences in container ports are multifractal, where the degree of multifractality is much higher for the port of Singapore compared with Shanghai and Rotterdam.  
The rest of the paper is organized as follows: Section 2 presents a brief review on the literature. Section 3 introduces the methodology used in this paper. Section 4 describes the sample data. Section 5 presents empirical results. Finally, Section 6 provides concluding observations based on the findings of the study.