Switching point of BPI -BPI -Linear1,a1=1.96096 --Linear2.a2=1.22985 w/- (s)) 0 0.5 1.0 15 2.0 2.5 Ig(s) Fig.9. Log-log plot of the fluctuation function with respect to time step(Ig(F(s))vs.Ig(s))of BPI in DFA2 test.a is the slope of fitting line. Table 3.Switching points Freight rate index lg(s)of switching points Time step S BPI 1.38021 24 BCI 1.50515 32 BSI 1.44716 28 Conclusion In this paper,we analyze the long memory feature of freight rate index time series under structural breaks. DFA and ICSS model are established and applied in the study of nonstationary BSI,BPI and BCI time series. For the sake of optimization of DFA method,we present the differences of different orders of DFA and conclude that DFA2 is appropriate in this study.Furthermore,although impact of seasonality on freight rate market is analyzed,we don't take it into account in long-range correlation evaluation since its influence is negligible.Additionally,long memory character and switching points of BSI,BPI and BCI time series are exhibited Our empirical results show that,in the time range from July Ist,2005 to February 26th,2015 BSI,BPI and BCI time series all have structural breaks,the most notable one of which exists around 2008.Thus,the advantage of DFA method used in our study is considerable,since DFA never calls for stability in time series. Besides,long-range correlation is also validated in BSI,BPI and BCI time series,proving the influence of current freight rate market condition on its next stage.Another finding is that load capacity has negative correlation with the long memory character of dry bulk carrier freight rate market.Capesize,as the largest in 1111 0.5 1.0 1.5 2.0 2.5 0 1 2 3 BPI Linear 1, =1.96096 Linear 2, 2=1.22985 lg(s) lg(F(s)) Switching point of BPI Fig. 9. Log-log plot of the fluctuation function with respect to time step ( lg( ( )) F s vs. lg( )s ) of BPI in DFA2 test.  is the slope of fitting line. Table 3. Switching points Freight rate index lg( )s of switching points Time step s BPI 1.38021 24 BCI 1.50515 32 BSI 1.44716 28 Conclusion In this paper, we analyze the long memory feature of freight rate index time series under structural breaks. DFA and ICSS model are established and applied in the study of nonstationary BSI, BPI and BCI time series. For the sake of optimization of DFA method, we present the differences of different orders of DFA and conclude that DFA2 is appropriate in this study. Furthermore, although impact of seasonality on freight rate market is analyzed, we don’t take it into account in long-range correlation evaluation since its influence is negligible. Additionally, long memory character and switching points of BSI, BPI and BCI time series are exhibited. Our empirical results show that, in the time range from July 1st, 2005 to February 26th, 2015 BSI, BPI and BCI time series all have structural breaks, the most notable one of which exists around 2008. Thus, the advantage of DFA method used in our study is considerable, since DFA never calls for stability in time series. Besides, long-range correlation is also validated in BSI, BPI and BCI time series, proving the influence of current freight rate market condition on its next stage. Another finding is that load capacity has negative correlation with the long memory character of dry bulk carrier freight rate market. Capesize, as the largest in