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1 : (2008) CCF ECM 1, 2, 2, 1,2 (11, ;21, ) : (CCF) Hong(2001) ( ECM) Granger. (Dubai) (Tapis) (Minas),,. Hong(2001), 10 %, WTI Brent Granger, WTI., Granger, Hong(2001) ECM. : ; ; ; ; ; ; GARCH : F06411 : A Information spillovers among international crude oil markets - An empirical analysis based on CCF method and ECM LU Feng2bin 1, LI Yi 2, WANG Shuan2hong 2, WANG Shou2yang 1,2 (11Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing , China ; 21School of management of Graduate School of the Chinese Academy of Sciences, Beijing , China) Abstract : Using Hong(2001) s method based on Cross Covariance Function ( CCF) and Error Correction Model ( ECM),we study Granger causality and information spillovers among major global crude oil markets including London, New York, Dubai as well as Tapis and Minas in Southeast Asia. The results show that London and New York futures markets play dominant roles in information spillover. And we find WTI crude oil futures has a slight edge over Brent crude oil futures in information transmission by employing methodology introduced by Hong. In addition, empirical results show Hong s method is more effective than ECM in testing Granger causality and information spillovers. Key words : crude oil futures ; Granger causality ; information spillover ; risk spillover ; cointegration ; ECM; GARCH 1,,,. 2003, %, %, %.,,2005 (WTI) %, 5617 ; ,.,, GDP,. ( IEA), 10,2006 GDP 018, 018.,,,., : : ; :,,, :.

2 ,,,. : Granger ;, CCF Hong (2001), ( ECM), Granger, Hong(2001) ;. 1. 2, Granger,. Brunetti & Gilbert (2000) FIGARCH IPE COMEX, NYMEX IPE, NYMEX. Lin & Tamvakis (2001) GARCH VAR IPE NYMEX,, IPE NYMEX, NYMEX IPE,,NYMEX IPE, IPE,. Hammoudeh et al. (2003) VECM GARCH NYMEX WTI, NYMEX. Hammoudeh & Li (2004) VECM Granger,,.,,. Lin & Tamvakis (2004) ACD IPE NYMEX, NYMEX. Chen et al. (2005),,. Tse & Xiang (2005) NYMEX ( E2Mini), 30 %.,. (2005) Hong(2001) (WTI),,. (2005) VAR Granger, 180 Granger,

3 3 CCF ECM 27 Granger. 3, (NYMEX) WTI ( IPE) (Brent) (Dubai).,,, %. ( ) ( Tapis) ( ICP, - Minas )., (Dubai) (Tapis) (Minas). IPE Brent (NYMEX) WTI Dubai Tapis Minas ; (Brent ),WTI WTI Cushing ,. r t = 100 (ln ( P t ) - ln ( P t - 1 ) ), P t.,, , ( )., WTI WTI,WTICush WTI Cushing,Brent IPE Brent,BrentS Brent,.,.,. Tapis ( ),Minas,Dubai, Brent,NYMEX, 1. IPE Brent WTI, ( 2 3). 1 ( ) Tapis Minas Dubai ( ) Brent 1 10 :02-10 :03 18 :02-18 :03 20 :12-20 :13 04 :12-04 : :03-10 :04 18 :03-18 :04 20 :11-20 :12 04 :11-04 : :05-10 :06 18 :05-18 :06 20 :09-20 :10 04 :09-04 :10 10 :06-10 :07 18 :06-18 :07 20 :08-20 :09 04 :08-04 :09 2 :00 10 :00 9 :45 17 :45 : Brent , GMT 1 :00-22 :00. 3 (WTI) 10 :00-14 :30 23 :00-3 :30 15 :15-9 :00 4 :15-22 :00 19 :00-9 :00 8 :00-22 :00 : 2 3 http :ΠΠinfo. china. alibaba. comπnewsπdetailπv4 - d html. 3,. Brent WTI ; IPE,,

4 :00-22 :00 ( 9 :00-6 :00), 3., Granger, Granger. 311 Hong( 2001) Hong CCF ( ),., 2Granger Q 1 ( M) : Q 1 ( M) = T k 2 ( jπm) ^ 2 ( j) - C 1 T ( k) Π(2 D 1 T ( k) ) 1Π2, j = 1 2Granger Granger, Q 2 ( M) : Q 2 ( M) = T k 2 ( jπm) ^ 2 ( j) - C 2 T ( k) Π(2 D 2 T ( k) ) 1Π2, j = 1- T ^ ( j) j, k ( x) k, M, C 1 T ( k) = C 2 T ( k) = j = 1 (1 - jπt) k 2 ( jπm), D 1 T ( k) = - j ΠT) k j = 1- T(1 2 ( jπm), D 2 T ( k) = j = 1- T j = 1 (1 - jπt) (1 - ( j + 1)ΠT) k 4 ( jπm), (1 - j ΠT) (1 - ( j + 1)ΠT) k 4 ( jπm). Hong(2001),., Granger.,, Daniell, k ( x) Daniell. :, Hong(2001)., GARCH : r t m = c + a t - i r t - i i = 1 + t, t t - 1 N (0, h t ), h t i t - i + = t t, t t, N (0, h t ) 0 h t. GARCH 4,Ljung2BOX Q. LB (M) 4 GARCH q i = 1 p j = 1 j h t - j, Tapis Minas Dubai Brent BrentS WTI WTICush c (010584) a (010338) (010590) (010148) (010245) [011827] [015263] (010686) (010341) (010698) (010138) (010223) [ ] [ ] (010606) (010334) (010621) (010095) (010225) [011759] [017053] (010638) (010334) (011167) (010137) (010378) [ ] [ ] (010718) (010343) (012996) (010211) (010747) [012547] [016123] : (),LB (M) M Ljung2Box, [ ] p (010671) (010334) (011065) (010118) (010325) [ ] [ ] (010732) (010354) (016447) (010377) (011587) [011446] [013495], ( Tapis & Minas) Dubai (Brent) (NYMEX WTI) 4, 4., Q 2 ( M) Granger, Q 1 ( M), 5 6,

5 3 CCF ECM 29 Q 1 ( M) (Brent WTI )., Q 2 ( M) 10 % 5 % Tapis ΖMinas Tapis Ζ Dubai Tapis ΖBrent Tapis Ζ WTI Minas Ζ Dubai Dubai ΖBrent Dubai ΖBrentS Dubai Ζ WTI Brent ΖBrentS Brent Ζ WTI BrentS Ζ WTICush : Ζ ; M 10 20, [ ] p, Q 1 ( M) 10 % 5 % Tapis Minas Tapis Minas [0161 ] [0176 ] [0151 ] 0116 [0144 ] 0136 [0136 ] 0135 [0136 ] [0187 ] [0190 ] Tapis Dubai Tapis Dubai 0189 [0119 ] 0154 [0130 ] 2144 [0101 ] 1153 [0106 ] 0138 [0135 ] 1113 [0113 ] 1104 [0115 ] 0151 [0130 ] Tapis Brent Tapis Brent Tapis BrentS Tapis BrentS

6 % 5 % Tapis WTI Tapis WTI Tapis WTICush [0109 ] [0101 ] 1136 [0109 ] Tapis WTICush Dubai Brent [0101 ] Dubai Brent Dubai BrentS Dubai BrentS Dubai WTI Dubai WTI Dubai WTICush [0123 ] 0167 [0125 ] Dubai WTICush Brent BrentS Brent BrentS [0159 ] [0177 ] [0180 ] [0174 ] [0173 ] [0172 ] [0157 ] [0155 ] Brent WTI [0152 ] 0118 [0143 ] [0170 ] [0167 ] [0176 ] [0169 ] [0170 ] [0151 ] Brent WTI [0176 ] [0183 ] 0130 [0138 ] 0125 [0140 ] 1153 [0106 ] 1131 [0109 ] 1154 [0106 ] 0163 [0126 ] BrentS WTICush BrentS WTICush [0140 ] 0180 [0121 ] WTI WTICush [0155 ] 0107 [0147 ] [0160 ] [0164 ] 1153 [0106 ] 0156 [0169 ] [0174 ] [0176 ] WTI WTICush 0112 [0145 ] 0102 [0149 ] [0188 ] [0191 ] [0185 ] [0175 ] [0179 ] [0165 ] :. 5,4, p 0,,. 6,, : 1) (Minas & Tapis) Minas Tapis, ;,, Tapis. Tapis Minas 1,

7 3 CCF ECM 31, Tapis, Tapis,. 2) (Brent &Brent spot), Brent p 0,,,.,. : ; Brent,,Brent. 3) (WTI & WTICush) 5 %, ; 10 %, WTI WTICush 10 % ;,,,,. 4),Tapis.,,,,,.,Tapis Dubai, 1 %., (Dubai),.,,. : 10 %, WTI Brent 10 % 5 %,,, WTI., Tapis Dubai,,. Hong(2001) :,, WTI ;Dubai., ECM, Tapsi Minas,,Dubai Tapis Brent. 312 ECM ECM, ( ),., ECM. ADF, 7 : 1 %,7 Brents,,., EG( Engle2Granger),,,, ECM.,, VECM,, ECM2GARCH : : y t = a + bx t + e t, : y t = c + 0 x t + e t - 1 p + i = 1 i y t - i p + i = 1 i x t - i, u t GRACH( p, q).,, 0 x y, x y y. 7 6 ECM( 8 13),. ( 1 20 Ljing2Box Q ;,, SC ) :

8 ADF Tapis Minas Dubai Brent BrentS WTI WTICush [01030 ] [01038] [01018 ] : [ ] PP p, : [01024 ] [010099] (Tapis Minas) ECM [01013 ] M t = T t + e t, gr 2 1 = T t = M t + e t, gr 2 1 = M t = [01557] T t e t - 1 u t N (0, h t ), gr 2 2 = h t = u 2 t h t - 1 T t = M t e t - 1 [01129 ] u t N (0, h t ), gr 2 2 = h t = u 2 t h t [01013] : ECM ( [ ] p )., M Minas, Ws Bs ;, e OLS, ; gr 2 1 gr 2 2 R ECM B t = Bs t + e t, gr 2 1 = Bs t = B t + e t, gr 2 1 = B t = Bs t e t Bs t - 1 [01043] [01392 ] B t - 1 u t N (0, h t ), gr 2 2 = B t - 2 h t = u 2 t h t - 1 Bs t = B t e t B t - 1 [01130] B t - 2 [01015] u t N (0, h t ), gr 2 2 = Bs t - 1 h t = u 2 t h t Bs t - 2 [01002 ] 10 ECM W t = Ws t + e t, gr 2 1 = Ws t = W t + e t, gr 2 1 = W t = Ws t e t Ws t - 1 [01608] [01884] W t - 3 [01001 ] u t N (0, ), gr 2 2 = Ws t = W t e t W t [01608 ] [01337 ] Ws t - 3 u t N (0, ), gr 2 2 = (Brent) (WTI) ECM B t = W t + e t, gr 2 1 = W t = B t + e t, gr 2 1 = B t = [01078] W t e t W t - 1 [01132 ] - W t = [01915 ] B t e t W t - 1 [01033] B t B t - 2 [01003 ] 0112 W t - 2 [01001] u t N (0, h t ), gr 2 2 = u t N (0, h t ), gr 2 2 = h t = u 2 t h t - 1 [010001] h t = u 2 t h t - 1

9 3 CCF ECM (Tapis) (WTI) ECM T t = W t + e t, gr 2 1 = W t = T t + e t, gr 2 1 = T t = [01051 ] Wt e t W t W t = T t e t T t [01298] [01251] T t T t - 2 u t N (0, h t ), gr 2 2 = T t - 3 [01005 ] h t = u 2 t h t - 1 [01017 ] W t - 1 u t N (0, h t ), gr 2 2 = h t = u 2 t h t - 1 [01927 ] [01002] 13 (Dubai) (WTI) ECM D t = W t + e t, gr 2 1 = W t = D t + e t, gr 2 1 = D t = W t e t W t [01075] [01027] D t - 1 u t N (0, h t ), gr 2 2 = 0146 h t = u2 t D t D t - 3 [01067 ] W t = D t e t D t [01560 ] [01001 ] [01231 ] W t W t - 2 [01012] u t N (0, h t ), gr 2 2 = h t = u 2 t h t - 1 [01359 ] 5, gr 2 1, ,.,,.,,,.,, ECM. (Tapis Minas) ECM Minas,Tapis 01988,, Tapis Minas Granger, Tapis Minas ; gr ,ECM, Tapis, Tapis Minas Granger. Tapis.,,,, SC,,. ECM,, Brent Granger., Brent, B t - 1 B t - 2, Brent, Bs t - 1, Brent, Granger, Granger.,,. ECM : Granger, Granger ;,Brent WTI Granger, Granger ; Tapis WTI, Tapis WTI, Granger,, Tapis,WTI Tapis, gr , WTI gr 2 2 ( = 01076), WTI Tapis Tapis WTI,, WTI ;,Dubai WTI Granger, WTI. ECM WTI Granger, Brent WTI Granger. 313

10 , Hong(2001) ECM, Granger. Hong(2001) Granger, ECM,.,, Granger,Hong(2001) Granger, ECM.,, NYMEX WTI IPE Brent Granger, WTI. Hong (2001), WTI Brent 10 %,,WTI Brent.,.,Lin & Tamvakis(2004) ACD NYMEX,. IPE NYMEX ACD,, ACD, Brent ACD, NYMEX., VECM Granger.,,,.,,.,,,,, Granger,..,,.,,. 4 Hong(2001) ECM Granger, :1) (WTI) (Brent) Granger, ;2) WTI Granger ;3) Brent Granger, Brent Granger, Brent Granger., Hong(2001), WTI WTI Brent,WTI., Granger,Hong(2001) ECM.,, Brent WTI., Brent ,,.. : [ 1 ] Granger C. Testing for causality : A personal view[j ]. Journal of Economic Dynamics and Control, 1980, 2 : [ 2 ] Hong Y. A test for volatility spillover with applications to exchange rates[j ]. Journal of Econometrics, 2001, 103 : [ 3 ] Bollerslev T. A generalized autoregressive conditional heteroskedasticity[j ]. Journal of Econometrics, 1986, 31 : [ 4 ] Brunetti C, Gilbert C. Bivariate FIGARCH and fractional cointegration[j ]. Journal of Empirical Finance, 2000, 7 : [ 5 ] Engle R, Granger C. Co2integration and error correction : Representation, estimation, and testing[j ]. Econometrica, 1987, 55 (2) : [ 6 ] Engle R, Russell J. Autoregressive conditional duration : A new model for irregularly spaced transaction data[j ]. Econometrica, 1998, 66 : [ 7 ] Lin S, Tamvakis M. Spillover effects in energy futures markets[j ]. Energy Economics, 2001, 23 : ( 43 )

11 3 43 : [ 1 ] Axsgter S. Modeling emergency lateral transshipment in inventory systems[j ]. Management Science, 1999, 36 : [ 2 ] Bowman J P. A multi2echelon inventory stocking algorithm for repairable items with lateral resupply[ Z]. Working Paper, [ 3 ] Cachon G P. Supply chain coordination with contracts[j ]. Chapter 6 in the Handbooks in Operations Research and Management Science : Supply Chain Management, S. Graves and T. Kok ( Eds. ), North2Holland, [ 4 ] Dada M. A two2echelon inventory system with priority shipments [ Z]. Working Paper,1985. [ 5 ] Deshpande V, Cohen M A, Donohue K. A threshold inventory rationing policy for service differentiated demand classes [J ]. Management Science,2003,49 : [ 6 ] Grahovac J,Chakravarty A. Sharing and lateral transshipment of inventory in a supply chain with expensive low2demand items[j ]. Management Science, 2001, 47 : [ 7 ] Lee H L. A multi2echelon inventory model for repairable items with emergency lateral transshipments[j ]. Management Science, 1987,33 : [ 8 ] McGill J I, Van Ryzin GJ. Revenue management : Research overview and prospects[j ]. Transportation Science, 1999, 33 (2) : [ 9 ] Nahmias S, Demmy W S. Operating characteristics of an inventory system with rationing[j ]. Management Science, 1981, 27 : [10 ] Slay F M. Lateral resupply in a multi2echelon inventory system[ C]ΠΠWorking Note, Logistics Management Instituie, Washington, D. C., [11 ] Talluri K T, Van Ryzin G J. The Theory and Practice of Revenue Management [M]. Kluwer Academic Publishers, New York, ( 34 ) [ 8 ] Hammoudeh S, Li H, Jeon B. Causality and volatility spillovers among petroleum prices of WTI, gasoline and heating oil in different locations[j ]. North American Journal of Economics and Finance, 2003, 14 : [ 9 ] Lin S, Tamvakis M. Effects of NYMEX trading on IPE brent crude futures markets : A duration analysis[j ]. Energy Policy, 2004, 32 : [10 ] Hammoudeh S, Li H. The impact of the Asian crisis on the behavior of US and international petroleum prices [J ]. Energy Economics, 2004, 26 : [11 ] Tse Y, Xiang J. Market quality and price discovery : Introduction of the E2mini energy futures[j ]. Global Finance Journal, 2005, 16 : [12 ] Bhara R, Hamori S. Causality in variance and the type of traders in crude oil futures[j ]. Energy Economics, 2005, 27 : [13 ],,,. [J ]., 2004, 3 (3) : [14 ],. [D]. 2005,,2005. [15 ]. [D].,,,2005. [16 ],. [M]. :,2000.

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