A.H.Alizadeh,N.K.Nomikos Transportation Research Part B 41 (2007)126-143 135 Table 3 Result of VECM for three size dry bulk carriers Ap: 〉aAp-4+>b△-+hP-1-r--o)+1r △：= cAp-+ d4-+2pr-l-m-l-o）+ Estimated model for: Capesize Panamax Handysize △p △元 △p, △T, △p, △元4 ai=1,2 -0.030 0.043 -0.028 0.078 -0.027 0.023 (-0.012) (-0.018) -0.011 -0.018 (-0.010) (-0.010) [-2.541 [2.421] [-2.402] [4.289] [-2.868] [2.214] △p-1 0.203 0.071 0.145 0.166 0.241 0.123 (-0.057 (-0.085) -0.056 -0.088 (-0.052) (-0.056) [3.579] [0.828] [2.579 [1.880] [4.608] [2.181] △t-1 0.142 0.358 0.144 0.319 0.208 0.416 (-0.039) (-0.059) -0.036 -0.056 (-0.049) (-0.053) [3.646] [6.092] [4.056 [5.697] [4.230] [7.875] R 0.153 0.129 0.123 0.140 0.189 0.196 Causality test Statistics p-Value DF Statistics p-Value DF Statistics p-Value DF △r,→△p 13.29 0.0001 2 16.45 {0.0001 2 18.16 {0.0001 2 Ap,一△： 0.685 0.408} 3.534 {0.060} 2 4.028 {0.045} 2 Sample period is January 1976 to September 2004 for the Handysize and Panamax series and April 1979 to September 2004 for the capesize series. Standard errors,in(),are corrected for serial correlation and/or heteroscedasticity using the Newey and West(1987)method. .Numbers in [are t-statistics;DF are the degrees of freedom for the causality tests. increase,thus restoring equilibrium in the market.The same pattern is evident in the panamax and handysize markets. More rigorous investigation of the interactions between the variables can be obtained by performing Granger causality tests,which are presented in the same table.According to the Granger(1986)representation theorem,if two price series are cointegrated,then causality must exist in at least one direction.Theoretically, we expect operational earnings to Granger-cause ship prices.We test such causality between the variables by imposing the appropriate restrictions on the VECM model.Tests for the joint significance of the lagged cross-market returns and error correction coefficients,confirm the conjecture that TC earnings Granger-cause ship prices.On the other hand,ship prices cause TC earnings only in the handysize market at the 5%level,and there is no evidence of causality at the 1%level. 4.1.Profitability of trading rules There can be unlimited number of ways to set up trading strategies based on MA or filter rules,depending on factors such as the variable on which the rule is applied,the length of MA series considered,and the dis- tance from the mean in the case of filter rules.However,we choose to apply two simple MA based rules to illustrate the importance of the price-earnings relationship(ratio)in determining ship prices and consequently market timing in the sale and purchase market for ships. Our trading strategy is based on the deviation of the log P/E ratio from its long-run mean.In order to determine the timing of sale and purchase,we devise two MA series using the deviation of log P/E ratio from its long-run mean,one slow [e.g.MA(12)or MA(6)]and one fast [MA(1)],as shown in Fig.2 for the panamax market.The difference between the two constructed MA series is then used as an indicator for buy and sellincrease, thus restoring equilibrium in the market. The same pattern is evident in the panamax and handysize markets. More rigorous investigation of the interactions between the variables can be obtained by performing Granger causality tests, which are presented in the same table. According to the Granger (1986) representation theorem, if two price series are cointegrated, then causality must exist in at least one direction. Theoretically, we expect operational earnings to Granger-cause ship prices. We test such causality between the variables by imposing the appropriate restrictions on the VECM model. Tests for the joint significance of the lagged cross-market returns and error correction coefficients, confirm the conjecture that TC earnings Granger-cause ship prices. On the other hand, ship prices cause TC earnings only in the handysize market at the 5% level, and there is no evidence of causality at the 1% level. 4.1. Profitability of trading rules There can be unlimited number of ways to set up trading strategies based on MA or filter rules, depending on factors such as the variable on which the rule is applied, the length of MA series considered, and the dis￾tance from the mean in the case of filter rules. However, we choose to apply two simple MA based rules to illustrate the importance of the price–earnings relationship (ratio) in determining ship prices and consequently market timing in the sale and purchase market for ships. Our trading strategy is based on the deviation of the log P/E ratio from its long-run mean. In order to determine the timing of sale and purchase, we devise two MA series using the deviation of log P/E ratio from its long-run mean, one slow [e.g. MA(12) or MA(6)] and one fast [MA(1)], as shown in Fig. 2 for the panamax market. The difference between the two constructed MA series is then used as an indicator for buy and sell Table 3 Result of VECM for three size dry bulk carriers Dpt ¼ Xq i¼1 aiDpti þXq i¼1 biDpti þ c1ðpt1 hpt1 h0Þ þ e1;t Dpt ¼ Xq i¼1 ciDpti þXq i¼1 diDpti þ c2ðpt1 hpt1 h0Þ þ e2;t Estimated model for: Capesize Panamax Handysize Dpt Dpt Dpt Dpt Dpt Dpt ci i = 1, 2 0.030 0.043 0.028 0.078 0.027 0.023 (0.012) (0.018) 0.011 0.018 (0.010) (0.010) [2.541] [2.421] [2.402] [4.289] [2.868] [2.214] Dpt1 0.203 0.071 0.145 0.166 0.241 0.123 (0.057) (0.085) 0.056 0.088 (0.052) (0.056) [3.579] [0.828] [ 2.579] [1.880] [4.608] [2.181] Dpt1 0.142 0.358 0.144 0.319 0.208 0.416 (0.039) (0.059) 0.036 0.056 (0.049) (0.053) [3.646] [6.092] [4.056] [5.697] [4.230] [7.875] R2 0.153 0.129 0.123 0.140 0.189 0.196 Causality test Statistics p-Value DF Statistics p-Value DF Statistics p-Value DF Dpt ! Dpt 13.29 {0.000} 2 16.45 {0.000} 2 18.16 {0.000} 2 Dpt ! Dpt 0.685 {0.408} 2 3.534 {0.060} 2 4.028 {0.045} 2 • Sample period is January 1976 to September 2004 for the Handysize and Panamax series and April 1979 to September 2004 for the capesize series. • Standard errors, in (Æ), are corrected for serial correlation and/or heteroscedasticity using the Newey and West (1987) method. • Numbers in [Æ] are t-statistics; DF are the degrees of freedom for the causality tests. A.H. Alizadeh, N.K. Nomikos / Transportation Research Part B 41 (2007) 126–143 135