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Garbade ilber(1983)garbade ilber Bigman Goldfarb chechman(1983) Maberly(1985) Elam Dixon 1988 Bigman Engle Granger 1987 Johansen 1988 Johansen Juselius 1990 Lai Lai 1991 Ghosh 1993 orenbery Zapaa 1997 Kavussanos Nomikos 1999 Haigh 2000 Hasbrouck(1995) 1995 1998 2002 Garbade ilber 1983 1 2 3 Johansen VECM

p p 10 + α Z 1 + α11 i) i + α12( i) i + i= 1 i= 1 = α ( ε 1 p p 20 + α Z 1 + α 21 i) i + α 22( i) i + i= 1 i= 1 = α ( ε 2 1 2 α 11( i ), α ( i) 12, α ( i) 21, α ( i) 22 Z 1 α α p AIC α α Granger α α Z 0 > 1 α α Granger 1 i α Granger 2 α i Granger χ 2 Hasbrouck(1995) VECM P 0 + ( ε ) τ + Ψ k = 1 = P ψ *( L) ε 3 P =, 2*1 P 0 2*1 τ = ( 1,1 ) 2*1 ( ) Ψ *( L) Ψ(1)ε

ψ Ψ(1) ε ε, ε ) ( = 1 2 Hasbrouck 1995ψε f 2 σ = ψπψ Π ε σ 2 f Π Cholesky Π = M M M Hasbrouck 1995 i i i σ 2 f i 2 ( ψm ) i = σ 2 f 2001 1 2 2003 12 31 726 726 669 {} {}

1. AD 1 AD 1.72 1.51-27.10-27.78-1.59-0.78-15.49-25.39-0.40-0.66-10.47-14.58 AD 5% AD -2.87 AD 1 5% AD 1 5% { } { } 2. 2 Johansen 5% 1% r 0 29.19 15.41 20.04 r 1 2.31 3.76 6.65 r 0 22.65 15.41 20.04 r 1 0.98 3.76 6.65 r 0 23.00 15.41 20.04 r 1 0.36 3.76 6.65 Johansen 2 r 0 r 1 3. Granger

3 Granger C 6.28 1.37 6.71 1.24 Z 1 0.01 0.31-0.12-2.49-0.46-6.52-0.06-0.68 1-0.16-2.53 0.004 0.06 2 0.47 7.47 0.04 0.56 1 0.27 4.49 0.08 1.13 2 Granger H 0 2 χ α ( i) = 0( i 1,2) 57.23 0 12 = α 21 ( i) = 0( i = 1,2) 0.60 0.74 Z.9859 178. 4773, 5% 1 = 1 0 1 3 Granger α α α α α <0 Z 1 0 Z 0 1 < 1 i ( i = 1,2) i ( i = 1,2) 2

χ 2 Granger 3 Granger α21 ( i) = 0( i = 1,2) α Granger 4 Granger C 0.57 0.29 0.82 0.31 Z 0.06 4.78 0.0020 0.12 1 0.31 7.24 0.16 2.71 1 0.10 2.60-0.03-0.49 2 0.21 6.36-0.0067-0.15 1 0.03 0.93 0.01 0.30 2 Granger H 0 2 χ α ( i) = 0( i 1,2,3,4) 40.64 0 12 = α ( i) = 0( i 1,2,3,4) 7.56 0.02 21 = Z.9846 173. 0411, 5% 1 = 1 0 1 4 Granger α α α α α

2 1 1 1 2 1 χ 2 Granger Granger 5 Granger C 5.34 1.34 4.90 0.72 Z 0.04 4.41-0.03-2.17 1 0.03 0.72 0.03 0.52 1 0.07 1.83 0.17 2.74 2 0.20 8.18 0.15 3.53 1 0.13 5.00 0.12 2.82 2 Granger H 0 2 χ α ( i) = 0( i 1,2,3,4) 90.03 0 12 = α ( i) = 0( i 1,2,3,4) 8.23 0.02 21 = Z.0284 457. 8827, 5% 1 = 1 1 1 5 Granger α α α α α α 1 ( i = 1,2) i

2 ) 5 Granger Granger 4. Hasbrouck Hasbrouck 1985 α 21 (2 6 Hasbrouck 1 24.35% 75.65% 0% 100% 2 23.83% 76.17% 0.96% 99.04% 3 22.88% 77.12% 1.87% 98.13% 4 23.36% 76.64% 3.65% 96.35% 5 22.58% 77.42% 5.99% 94.01% n 13.18% 86.82% 12.75% 87.25% 6 Hasbrouck 6 1 24.35% 75.65% 13.18% 86.82% 1 12.75% 87.25% 12.97% = 13.18%+12.75% /2 87.03%(=(86.82%+87.25%)/2)

7 Hasbrouck 1 66.91% 33.09% 0% 100% 2 50.77% 49.23% 2.47% 97.53% 3 44.98% 55.02% 3.36% 96.64% 4 40.67% 59.33% 3.59% 96.41% 5 36.96% 63.04% 4.20% 95.80% n 15.17% 84.83% 14.35% 85.65% 7 Hasbrouck 7 1 66.91% 33.09% 15.17% 84.83% 1 14.35% 85.65% 14.76% = 15.17%+14.35% /2 85.24%(=(84.83%+85.65%)/2) 8 Hasbrouck 1 94.30% 5.70% 0% 100% 2 78.78% 21.22% 0.30% 99.70% 3 69.35% 30.65% 2.15% 97.85% 4 64.72% 35.28% 2.77% 97.23% 5 62.00% 38.00% 4.58% 95.42% n 21.60% 78.40% 19.90% 80.10%

8 Hasbrouck 8 1 94.30% 5.70% 21.60% 78.40% 1 19.90% 80.10% 20.75% = 21.60%+19.90% /2 79.25%(= (78.40%+80.10%)/2) 5. Impulse Responses Pesaran hin 1997 GIR Generalised Impulse Responses Cholesky 140 120 120 100 80 60 40 100 80 60 40 20 1 2 3 4 5 6 7 8 9 10 20 1 2 3 4 5 6 7 8 9 10 1 2 1 2 1

2 45 40 35 30 25 20 15 10 1 2 3 4 5 6 7 8 9 10 36 34 32 30 28 26 24 1 2 3 4 5 6 7 8 9 10 3 4 3 4 3 5 6 4 45 40 35 30 25 20 15 1 2 3 4 5 6 7 8 9 10 48 44 40 36 32 28 24 1 2 3 4 5 6 7 8 9 10 5 6 5 6 5 6

87.03% 12.97%; 85.24% 14.76% 79.25% 20.75% 1 Bigman, D. Goldfarb, D. and chechman, E. uures Marke Efficiency and he Time Conen of he Informaion es. Journal of uures Markes 3, 1983, pp. 321-334. 2 Elam, E, and Dixon, B. L. Examining he Validiy of a Tes of uures Marke Efficiency. Journal of uures Markes 8, 1988, pp. 365-372. 3 Engle, R., and Granger, C. W. J. Coinegraion and Error Correcion Represenaion, Esimaion and Tesing. Economerica 55, 1987, pp. 251-276. 4 orenbery, T. R. and Zapaa, H. O. An Evaluaion of Price Linkages beween uures and Cash Markes for Cheddar Cheese. Journal of uures Markes 17, 1997, pp. 279-301. 5 Garbade, K. D. and ilber, W. L. Price Movemens and Cash Discovery in uures and Cash Markes. Review of Economics and aisics 65, 1983, pp. 289-297. 6 Ghosh, A. Coinegraion and Error Correcion Models: Ineremporal Causaliy beween Index and uures Prices. Journal of uures Markes 13, 1993, pp. 193-198. 7 Haigh, M.. Coinegraion, Unbiased Expecaions, and orecasing in he BIEX reigh uures Marke. Journal of uures Markes 6, 2000, pp. 545-571. 8 Hasbrouck, J. One ecuriy, Many Markes: Deermining he Conribuions o Price Discovery. Journal of inance 50, 1995, pp. 1175-1199.

9 Johansen,. aisical Analysis of Coinegraing Vecors. Journal of Economic Dynamics and Conrol 12, 1988, pp. 231-254. 10 Johansen,.and Juselius, K. Maximum Likelihood Esimaion and Inference on Coinegraion-wih Applicaions o he Demand for Money. Oxford Bullein of Economics and aisics 52, 1990, pp. 169-210. 11 Kavussanos, M. and Nomikos, N. The orward Pricing uncion of he hipping reigh uures Marke. Journal of uures Markes 19, 1999, pp. 353-376. 12 Lai, K. and Lai, M. A Coinegraion Tes for Marke Efficiency. Journal of uures Markes 11, 1991, pp. 567-575. 13 Maberly, E. D. Tesing uures Marke Efficiency, A Resaemen. Journal of uures Markes 5, 1985, pp. 425-432. 14 Pesaran, M. H, and hin, Y. Generalised Impulse Response Analysis in Linear Mulivariae Models. Working Paper, Cambridge Universiy, 1997. 15 1998 12 162002 5 17 1995 8