95 06
...1...1...3...5...6...7...7...10...13...13...14...14...15...17...18...19...22...22
...22...27...31...41...53...61...61...63...64
1
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VAR VAR Johansen VECM 6
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12
E( y ) = E( y ) = u t t+ n y E( y u ) = E[( y u ) ] = σ 2 2 2 t y t+ n y y COV ( yt, yt+ k) = γ k 13
k t t 1 i t 1 t i= 1 X = ρ X + β X + ε k i= 1 Xt = α + ρxt 1 + βi Xt 1 + εt k Xt = α + δt + ρxt 1 + βi Xt 1 + εt i= 1 14
2 2k AIC = AIC = ln( σ ) + T 2 2k SBIC = ln( σ ) + lnt T 2 σ H : ρ = 0 0 τ ρ 15
Y X p = α + α Y + β X + ε t 10 1i t i 1j t j 1t i= 1 j= 1 p q = α + α Y + β X + ε t 20 2i t i 2 j t j 2t i= 1 j= 1 q ε1t ε 2t H H : β = β = = β = 0 0 11 12 1q ' 0 β21 β22 β2q : = = = = 0 H0 ' H0 ' H0 H0 16
X = A + AX + e t 0 n i= 0 i t i t X t A 0 A X Xt i t-i 2 e t et σ x et e t-i e 1t e 2t 17
X AX AX AY = A + e t 1 t 1 2 t 2 p t p 0 t 2 p AL 1 AL 2 ApL Xt = A0+ et (1 ) 2 p 1 Xt = (1 AL 1 AL 2 AL p ) ( A0+ et) X µ Ce i= 0 = + t i t i 18
X µ ' t = + CVV i et i i= 0 ε t-i C i = CV i ε ' t-i = Ve t i X = µ + C ε t i t i i= 0 C i 19
Y t X t Y = β + β X + u t 0 1 t u I(0) t Xt = β + 1 Xt 1+ k Xt k + ε X t q 1 X t-i i = 1,, k ε 2 t iid... N(0, σ ) β i, i = 1,, k t X i Xt = β +Γ Xt 1+ +Γ k 1Xt k+ 1+ Xt k+ ε k 1 β + Γ X + X + ε i 1 i t i t k Γ i = ( I 1 i), i= 1,, k 1 X t 20
= ( I 1 k ) X t X t X t X t X t X t X t H0 n λ ( q) = T ln(1 λ ) trace i= r+ 1 i 21
τ 22
23
4.24 4.20 4.16 4.12 4.08 4.04 2000M04 2003M01 2004M10 DOW.05.04.03.02.01.00 -.01 -.02 -.03 -.04 2000M04 2003M01 2004M10 SPREAD 1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.2 2000M04 2003M01 2004M10 OIL 1.85 1.80 1.75 1.70 1.65 1.60 1.55 1.50 1.45 2000M04 2003M01 2004M10 CHEVRON 1.85 1.80 1.75 1.70 1.65 1.60 1.55 1.50 1.45 2000M04 2003M01 2004M10 EXXON 2.0 1.8 1.6 1.4 1.2 1.0 2000M04 2003M01 2004M10 CONOCO 24
1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.2 2000M04 2003M01 2004M10 MARATHON 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 1.0 2000M04 2003M01 2004M10 MURPHY 25
τ 26
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Response of DEXXON to Cholesky One S.D. Innovations Response of DDOW to Cholesky One S.D. Innovations.016.012.012.010.008.008.006.004.004.002.000.000 -.004 1 2 3 4 5 -.002 1 2 3 4 5 DEXXON DDOW SPREAD DOIL DEXXON DDOW SPREAD DOIL Response of SPREAD to Cholesky One S.D. Innovations Response of DOIL to Cholesky One S.D. Innovations.005.025.004.020.003.015.002.010.001.005.000.000 -.001 1 2 3 4 5 -.005 1 2 3 4 5 DEXXON DDOW SPREAD DOIL DEXXON DDOW SPREAD DOIL 35
.014 Response of DCHEVRON to Cholesky One S.D. Innovations.012 Response of DDOW to Cholesky One S.D. Innovations.012.010.010.008.006.004.002.008.006.004.002.000.000 -.002 1 2 3 4 -.002 1 2 3 4 DCHEVRON DDOW SPREAD DOIL DCHEVRON DDOW SPREAD DOIL.006 Response of SPREAD to Cholesky One S.D. Innovations.025 Response of DOIL to Cholesky One S.D. Innovations.005.020.004.015.003.002.010.001.005.000.000 -.001 1 2 3 4 -.005 1 2 3 4 DCHEVRON DDOW SPREAD DOIL DCHEVRON DDOW SPREAD DOIL 36
Response of DCONOCO to Cholesky One S.D. Innovations Response of DDOW to Cholesky One S.D. Innovations.024.012.020.010.016.008.012.006.008.004.004.002.000.000 -.004 1 2 3 4 -.002 1 2 3 4 DCONOCO DDOW SPREAD DOIL DCONOCO DDOW SPREAD DOIL Response of SPREAD to Cholesky One S.D. Innovations Response of DOIL to Cholesky One S.D. Innovations.006.025.005.020.004.015.003.002.010.001.005.000.000 -.001 1 2 3 4 -.005 1 2 3 4 DCONOCO DDOW SPREAD DOIL DCONOCO DDOW SPREAD DOIL 37
Response of DMARATHON to Cholesky One S.D. Innovations Response of DDOW to Cholesky One S.D. Innovations.020.012.016.010.012.008.008.006.004.004.002.000.000 -.004 1 2 3 4 -.002 1 2 3 4 DMARATHON DDOW SPREAD DOIL DMARATHON DDOW SPREAD DOIL Response of SPREAD to Cholesky One S.D. Innovations Response of DOIL to Cholesky One S.D. Innovations.006.025.005.020.004.015.003.002.010.001.005.000.000 -.001 1 2 3 4 -.005 1 2 3 4 DMARATHON DDOW SPREAD DOIL DMARATHON DDOW SPREAD DOIL 38
Response of DMURPHY to Cholesky One S.D. Innovations Response of DDOW to Cholesky One S.D. Innovations.020.012.016.010.012.008.008.006.004.004.002.000.000 -.004 1 2 3 4 -.002 1 2 3 4 DMURPHY DDOW SPREAD DOIL DMURPHY DDOW SPREAD DOIL Response of SPREAD to Cholesky One S.D. Innovations Response of DOIL to Cholesky One S.D. Innovations.006.025.005.020.004.015.003.002.010.001.005.000.000 -.001 1 2 3 4 -.005 1 2 3 4 DMURPHY DDOW SPREAD DOIL DMURPHY DDOW SPREAD DOIL 39
.016 Response of DEXXON to Cholesky One S.D. Innovations.010 Response of DCHEVRON to Cholesky One S.D. Innovations.012.008.004.000.008.006.004.002.000 -.004 1 2 3 4 5 6 7 -.002 1 2 3 4 5 6 7.016.012.008.004.000 DEXXON DCHEVRON DCONOCO DMARATHON DMURPHY Response of DCONOCO to Cholesky One S.D. Innovations.012.010.008.006.004.002.000 DEXXON DCHEVRON DCONOCO DMARATHON DMURPHY Response of DMARATHON to Cholesky One S.D. Innovations -.004 1 2 3 4 5 6 7 -.002 1 2 3 4 5 6 7.012.010 DEXXON DCHEVRON DCONOCO DMARATHON DMURPHY Response of DMURPHY to Cholesky One S.D. Innovations DEXXON DCHEVRON DCONOCO DMARATHON DMURPHY.008.006.004.002.000 -.002 1 2 3 4 5 6 7 DEXXON DCHEVRON DCONOCO DMARATHON DMURPHY 40
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.5.6.4.3.2.4.2.1.0.0 -.1 -.2 -.2 -.4 -.3 50 100 150 200 250 300 -.6 50 100 150 200 250 300 Recursive C(1) Estimates ± 2 S.E. Recursive C(2) Estimates ± 2 S.E..3.5.2.4.3.1.2.1.0.0 -.1 -.1 -.2 -.2 50 100 150 200 250 300 -.3 50 100 150 200 250 300 Recursive C(3) Estimates ± 2 S.E. Recursive C(4) Estimates ± 2 S.E..4.2.0 -.2 -.4 -.6 -.8 50 100 150 200 250 300 Recursive C(5) Estimates ± 2 S.E. 51
4 2 3 1 2 0-1 1-2 0-3 -1 50 100 150 200 250 300-4 50 100 150 200 250 300 Recursive C(1) Estimates ± 2 S.E. Recursive C(2) Estimates ± 2 S.E. 1.6 3 1.2 2 0.8 1 0.4 0.0 0-0.4-1 -0.8 50 100 150 200 250 300-2 50 100 150 200 250 300 Recursive C(3) Estimates ± 2 S.E. Recursive C(4) Estimates ± 2 S.E. 2 1 0-1 -2-3 50 100 150 200 250 300 Recursive C(5) Estimates ± 2 S.E. 52
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