罗 X.Zhang et aL Physica A 415 (2014)43-53 ship market(blue solid line circle Fig.1(b)).Fig.2(b)shows a structure that differs greatly from that in Fig.2(a).We see that (i)freight rates for several dry bulk carriers,container ships,and oil tankers are closely correlated and form a tight cluster with shorter distances,indicating that during the crisis period the second-hand ship prices of a certain ship type are determined both by its own supply-and-demand and by freight rates of other ship types(the red block in Fig.2(b)):(ii) prices of new container carriers,dry bulk carriers,and tankers cross the boundaries previously separating them and move together,which can be found in the green block in Fig.2(b);and (iii)a third cluster,made up of second-hand container ship prices and second-hand Panamax oil tanker prices,that indicates a close business connection between oil transport and container transport(the blue block in Fig.2(b)). In the post-crisis period the shipping market is no longer fragments.Fig.1(c)shows that the new ship markets form one independent group(red solid line circle),while the freight rate and second-hand ship price indicators tend to split into groups based on the three major ship types,that are oil tanker ship(green dash line circle).dry bulk ship(blue dash line circle)and container ship(red dash line circle).Fig.2(c)shows that second-hand container ship prices link to form the first cluster(the red block).freight rates of container transport vessels form a second cluster(the green block),and the prices of new crude oil tankers form a third(the blue block).Fig.1(c)also shows that the boundaries separating submarkets reappear in the post-crisis period. 5.Causality analysis of the shipping industry 5.1.Granger causality analysis To shed additional light on the structure and dynamics of the shipping industry,we implement Granger causality using the monthly returns of indices of the new ship market,the second-hand ship market,the freight market,and the shipping stock market prices for the pre-crisis,crisis,and post-crisis periods.Fig.3 shows the linear Granger causality relationships between months t and t +1 among the monthly indexes return of (i)the new ship market,(ii)the second-hand ship market,(iii)the freight shipping market,and(iv)shipping stock market prices for three periods,2003-2006,2007-2010,and 2011-2013.There are no significant bi-directional causal relationships among the four markets during the pre-crisis period. During the crisis period,however,all four markets become highly linked.During that period bi-directional relationships between the new ship market and the second-hand ship market,as well as between the second-hand ship market and the freight market emerge.All three shipping markets affect the shipping market stock price,and the new ship market influences the freight market.Thus shocks to real shipping markets easily propagate to stock market prices.During the earlier period, 2003-2006,only freight rate fluctuations affect stock market prices.During the post-crisis period,all four markets tend to become distant and there is only one significant bi-directional causal relationship remaining,the one between the second- hand ship market and the freight market.Stock market prices in the post-crisis period are much more independent than during the crisis period,and are influenced only by freight rate fluctuations. 5.2.Brownian distance correlation analysis Granger causality previously applied shows only linear directional interdependence,and next we further utilize Brownian distance correlation to explore non-linear directional interconnectedness among market sectors.Fig.4 shows Brownian distance correlation between months t and t+1(I=1,2,and 3)among the monthly return indexes of(i)the new ship market,(ii)the second-hand ship market,(iii)the freight shipping market,and (iv)shipping stock market prices for three periods,2003-2006,2007-2010,and 2011-2013.For the pre-crisis period,the Brownian distance correlation recognizes bi-directional causal relationships between the new ship market and the second-hand ship market.In contrast,Granger causality only shows that the second-hand ship market causes the changes of the new ship market in the same period (see Fig.4(a)).During the crisis period,the Brownian distance also captures more bi-directional dependent relationships, which are not significant in the Granger causality test.A feedback interdependence relationship can be observed among all four markets.Moreover bi-directional interdependence between the new-building ship market and the second-hand ship market as well as the new-building ship market and the freight market are both significant at time lag I =1,2 and 3. indicating the strong interaction effect among these markets.Additionally,feedback interdependence between the new- building ship market and the shipping stock market lasts for two time lags (I=1 and 2).but is not significant when I=3.During the post-crisis period,all causality relationships are significant only when the time lag is the one when Brownian distance explores bi-directional causal relationships between the new ship market and the second-hand ship market,which are also not recognized by the Granger causality analysis(see Fig.4(c)).Brownian distance correlation is a natural extension and generalization of classical Person correlation to measure non-linear association to multivariate dependence.Through preview tests,researchers find that in most cases Brownian distance correlation results show strong significant correlation than Granger causality and Person correlation 43.So this phenomenon is not unique in the shipping market,but the difference between Brownian distance and classical correlation measurements mainly depends on the market characteristics.48 X. Zhang et al. / Physica A 415 (2014) 43–53 ship market (blue solid line circle Fig. 1(b)). Fig. 2(b) shows a structure that differs greatly from that in Fig. 2(a). We see that (i) freight rates for several dry bulk carriers, container ships, and oil tankers are closely correlated and form a tight cluster with shorter distances, indicating that during the crisis period the second-hand ship prices of a certain ship type are determined both by its own supply-and-demand and by freight rates of other ship types (the red block in Fig. 2(b)); (ii) prices of new container carriers, dry bulk carriers, and tankers cross the boundaries previously separating them and move together, which can be found in the green block in Fig. 2(b); and (iii) a third cluster, made up of second-hand container ship prices and second-hand Panamax oil tanker prices, that indicates a close business connection between oil transport and container transport (the blue block in Fig. 2(b)). In the post-crisis period the shipping market is no longer fragments. Fig. 1(c) shows that the new ship markets form one independent group (red solid line circle), while the freight rate and second-hand ship price indicators tend to split into groups based on the three major ship types, that are oil tanker ship (green dash line circle), dry bulk ship (blue dash line circle) and container ship (red dash line circle). Fig. 2(c) shows that second-hand container ship prices link to form the first cluster (the red block), freight rates of container transport vessels form a second cluster (the green block), and the prices of new crude oil tankers form a third (the blue block). Fig. 1(c) also shows that the boundaries separating submarkets reappear in the post-crisis period. 5. Causality analysis of the shipping industry 5.1. Granger causality analysis To shed additional light on the structure and dynamics of the shipping industry, we implement Granger causality using the monthly returns of indices of the new ship market, the second-hand ship market, the freight market, and the shipping stock market prices for the pre-crisis, crisis, and post-crisis periods. Fig. 3 shows the linear Granger causality relationships between months t and t + 1 among the monthly indexes return of (i) the new ship market, (ii) the second-hand ship market, (iii) the freight shipping market, and (iv) shipping stock market prices for three periods, 2003–2006, 2007–2010, and 2011–2013. There are no significant bi-directional causal relationships among the four markets during the pre-crisis period. During the crisis period, however, all four markets become highly linked. During that period bi-directional relationships between the new ship market and the second-hand ship market, as well as between the second-hand ship market and the freight market emerge. All three shipping markets affect the shipping market stock price, and the new ship market influences the freight market. Thus shocks to real shipping markets easily propagate to stock market prices. During the earlier period, 2003–2006, only freight rate fluctuations affect stock market prices. During the post-crisis period, all four markets tend to become distant and there is only one significant bi-directional causal relationship remaining, the one between the second￾hand ship market and the freight market. Stock market prices in the post-crisis period are much more independent than during the crisis period, and are influenced only by freight rate fluctuations. 5.2. Brownian distance correlation analysis Granger causality previously applied shows only linear directional interdependence, and next we further utilize Brownian distance correlation to explore non-linear directional interconnectedness among market sectors. Fig. 4 shows Brownian distance correlation between months t and t + l (l = 1, 2, and 3) among the monthly return indexes of (i) the new ship market, (ii) the second-hand ship market, (iii) the freight shipping market, and (iv) shipping stock market prices for three periods, 2003–2006, 2007–2010, and 2011–2013. For the pre-crisis period, the Brownian distance correlation recognizes bi-directional causal relationships between the new ship market and the second-hand ship market. In contrast, Granger causality only shows that the second-hand ship market causes the changes of the new ship market in the same period (see Fig. 4(a)). During the crisis period, the Brownian distance also captures more bi-directional dependent relationships, which are not significant in the Granger causality test. A feedback interdependence relationship can be observed among all four markets. Moreover bi-directional interdependence between the new-building ship market and the second-hand ship market as well as the new-building ship market and the freight market are both significant at time lag l = 1, 2 and 3, indicating the strong interaction effect among these markets. Additionally, feedback interdependence between the new￾building ship market and the shipping stock market lasts for two time lags (l = 1 and 2), but is not significant when l = 3. During the post-crisis period, all causality relationships are significant only when the time lag is the one when Brownian distance explores bi-directional causal relationships between the new ship market and the second-hand ship market, which are also not recognized by the Granger causality analysis (see Fig. 4(c)). Brownian distance correlation is a natural extension and generalization of classical Person correlation to measure non-linear association to multivariate dependence. Through preview tests, researchers find that in most cases Brownian distance correlation results show strong significant correlation than Granger causality and Person correlation [43]. So this phenomenon is not unique in the shipping market, but the difference between Brownian distance and classical correlation measurements mainly depends on the market characteristics