1 some pitfalls in testing … japan imports of wheat us pacific and gulf export ports
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Some Pitfalls in Testing …Some Pitfalls in Testing …
Japan Imports of WheatJapan Imports of Wheat
US Pacific and Gulf Export PortsUS Pacific and Gulf Export Ports
22
# 2 Hard # 2 Western #2 DNS # 2 Hard # 2 Western # 2 DNS # 2 DNS Freight Freight FFRDate Winter 13% White 14% Winter 13% White 13% 14% Gulf Pacific
Gulf Pacific Gulf Pacific75.09 207 182 217 176 162 187 201 15.74 13.28 6.24
75.1 207 182 220 178 161 184 199 17.22 13.78 5.82 World Wheat Statistics 197875.11 189 168 198 161 145 173 186 17.22 14.76 5.22 World Wheat Statistics 197875.12 172 156 197 151 141 178 178 16.73 14.51 5.2 World Wheat Statistics 197876.01 180 157 195 151 141 178 178 12.79 14.51 4.87 World Wheat Statistics 197876.02 192 164 201 166 151 186 186 14.76 13.53 4.77 World Wheat Statistics 197876.03 188 162 196 168 146 182 181 15.74 14.51 4.84 World Wheat Statistics 197876.04 177 148 185 156 138 162 175 15.74 13.78 4.82 World Wheat Statistics 197876.05 170 142 189 148 132 164 178 14.76 15.01 5.29 World Wheat Statistics 197876.06 174 147 193 154 134 173 181 15.01 15.01 5.48 World Wheat Statistics 197876.07 177 147 193 158 134 166 178 16.73 15.01 5.31 World Wheat Statistics 197876.08 158 140 174 137 126 142 156 15.74 15.25 5.29 World Wheat Statistics 197876.09 154 137 155 133 123 138 146 15.99 15.25 5.25 World Wheat Statistics 1978
76.1 154 127 146 119 112 131 134 16.24 15.25 5.03 World Wheat Statistics 197876.11 136 122 144 117 111 129 131 16.97 15.25 4.95 World Wheat Statistics 197876.12 131 115 135 115 105 136 125 16.24 14.27 4.65 World Wheat Statistics 197877.01 133 119 138 118 108 137 126 13.78 14.76 4.61 World Wheat Statistics 197877.02 134 121 141 118 111 140 130 13.78 14.76 4.68 World Wheat Statistics 197877.03 133 121 141 114 110 136 131 13.78 14.02 4.69 World Wheat Statistics 197877.04 124 121 141 109 110 122 129 13.78 14.02 4.73 World Wheat Statistics 197877.05 124 119 135 101 110 115 125 14.37 14.02 5.35 World Wheat Statistics 197877.06 116 112 129 97 104 107 117 13.78 14.02 5.39 World Wheat Statistics 197877.07 117 118 125 101 108 104 115 13.78 13.78 5.42 World Wheat Statistics 197877.08 114 120 125 98 108 102 115 14.27 13.78 5.9 World Wheat Statistics 197877.09 122 118 130 104 105 112 119 13.78 13.53 6.14 World Wheat Statistics 1978
77.1 128 115 134 108 105 117 123 14.02 13.53 6.47 World Wheat Statistics 197877.11 133 121 140 117 109 125 127 14.51 13.53 6.51 World Wheat Statistics 197877.12 135 124 140 118 111 134 127 15.01 14.76 6.56 World Wheat Statistics 197878.01 136 130 143 120 117 137 131 15.25 14.76 6.7 World Wheat Statistics 198178.02 138 136 146 122 124 137 134 14.51 13.53 6.78 World Wheat Statistics 198178.03 139 138 142 127 128 138 134 14.76 13.53 6.79 World Wheat Statistics 198178.04 150 148 142 135 136 145 140 14.76 13.53 6.89 World Wheat Statistics 198178.05 150 146 152 129 135 144 143 19.68 13.78 7.36 World Wheat Statistics 198178.06 147 146 152 130 136 139 143 20.66 14.02 7.6 World Wheat Statistics 198178.07 147 155 154 130 141 132 139 18.7 14.27 7.81 World Wheat Statistics 198178.08 149 150 149 130 139 131 138 19.14 14.27 8.04 World Wheat Statistics 198178.09 154 152 152 134 141 138 142 22.63 14.51 8.45 World Wheat Statistics 1981
78.1 154 152 152 139 141 143 144 22.14 15.25 8.96 World Wheat Statistics 198178.11 162 156 163 151 141 149 148 22.14 16.24 9.76 World Wheat Statistics 198178.12 164 159 166 138 140 153 150 22.14 17.47 10.03 World Wheat Statistics 198179.01 163 157 166 140 140 153 149 21.89 17.47 10.07 World Wheat Statistics 198179.02 165 153 166 144 137 153 151 21.89 17.47 10.06 World Wheat Statistics 198179.03 165 155 168 143 139 150 155 24.11 18.2 10.09 World Wheat Statistics 198179.04 167 157 168 141 139 146 152 24.11 18.2 10.01 World Wheat Statistics 198179.05 185 167 185 146 147 155 161 24.11 19.19 10.24 World Wheat Statistics 198179.06 203 193 212 164 166 174 184 28.54 27.55 10.29 World Wheat Statistics 198179.07 217 210 228 179 178 189 193 36.41 29.52 10.47 World Wheat Statistics 198179.08 218 200 214 173 171 180 185 34.44 28.63 10.94 World Wheat Statistics 198179.09 214 197 219 180 163 185 187 34.44 28.78 11.43 World Wheat Statistics 1981
79.1 221 194 223 183 161 188 189 34.44 29.47 13.77 World Wheat Statistics 198179.11 223 194 221 183 158 189 186 34.44 29.47 13.18 World Wheat Statistics 198179.12 222 194 220 185 157 194 187 34.44 29.52 13.78 World Wheat Statistics 198180.01 213 194 215 179 161 191 181 34.44 29.52 13.82 World Wheat Statistics 198180.02 217 196 219 176 163 189 184 34.44 29.03 14.13 World Wheat Statistics 198180.03 216 194 220 169 158 180 182 34.44 30.01 17.19 World Wheat Statistics 198180.04 210 190 211 158 155 166 176 43.3 30.01 17.61 World Wheat Statistics 198180.05 212 182 221 163 148 176 188 43.3 32.47 10.98 World Wheat Statistics 198180.06 212 180 224 159 148 174 190 37.39 32.47 9.47 World Wheat Statistics 198180.07 219 190 240 168 156 195 207 37.15 31.83 9.03 World Wheat Statistics 198180.08 229 192 239 175 158 192 205 37.88 31.83 9.61 World Wheat Statistics 198180.09 230 193 244 183 162 197 212 37.88 31.83 10.87 World Wheat Statistics 1981
80.1 239 203 249 192 171 204 218 37.88 31.83 12.81 World Wheat Statistics 198180.11 252 214 251 200 179 212 218 39.85 26.08 15.85 World Wheat Statistics 198180.12 232 211 245 188 171 212 206 39.85 29.77 18.9 World Wheat Statistics 198181.01 244 210 246 193 172 218 210 39.85 30.01 19.08 World Wheat Statistics 198281.02 234 210 242 185 172 216 207 39.85 30.01 15.93 World Wheat Statistics 198281.03 225 200 237 177 166 196 203 36.41 29.77 14.7 World Wheat Statistics 198281.04 225 201 249 183 169 191 214 36.41 29.77 15.72 World Wheat Statistics 198281.05 214 197 244 176 166 187 213 34.44 29.77 18.52 World Wheat Statistics 198281.06 220 189 232 172 161 183 202 36.16 29.77 19.1 World Wheat Statistics 198281.07 217 192 221 173 160 177 192 36.16 28.78 19.04 World Wheat Statistics 198281.08 216 194 219 174 161 173 186 31.49 28.29 17.82 World Wheat Statistics 198281.09 212 193 217 175 159 176 183 22.14 28.29 15.87 World Wheat Statistics 1982
81.1 216 197 216 175 164 180 184 24.6 28.29 15.08 World Wheat Statistics 198281.11 0 0 0 0 0 0 0 0 0 0
Data
33
ContentsContents Table ThreeTable Three
DNS Pacific: p. 4DNS Pacific: p. 4 DNS Gulf: p. 25DNS Gulf: p. 25 HW Gulf: P. 80HW Gulf: P. 80 WW Pacific: p.123WW Pacific: p.123
Table FourTable Four DNS Pacific: p.46DNS Pacific: p.46 DNS Gulf: p.63DNS Gulf: p.63 HW Gulf: p.100HW Gulf: p.100 WW Pacific: p. 143WW Pacific: p. 143
44
Table Three: Pacific DNSTable Three: Pacific DNS Log of Ratio of Import Price to Pacific Export Log of Ratio of Import Price to Pacific Export
Price (lag 1) Plus Pacific Freight (lag2)Price (lag 1) Plus Pacific Freight (lag2) StationaryStationary
No unit rootNo unit root AR (1) Model: root 0.54, normal residualAR (1) Model: root 0.54, normal residual
Log of Import Price and Log of Pacific Import Log of Import Price and Log of Pacific Import Price (lag 1) Plus Pacific Freight (lag 2)Price (lag 1) Plus Pacific Freight (lag 2) CointegratedCointegrated
VEC: one lagVEC: one lag Rank: 1, 1, 1, 1, 2Rank: 1, 1, 1, 1, 2 Data: no trend; Integrating Equation: Intercept, no trend, rank Data: no trend; Integrating Equation: Intercept, no trend, rank
one, 1%one, 1%
55
Trace of Import Price and Pacific Export Price (lagged one) Plus Pacific Freight Rate (lagged two), DNS, $/Metric Ton
0
50
100
150
200
250
300
Date
$/M
etr
ic T
on
DNSJ
DNSPJT
66
Trace of Import Price Minus the Sum of Pacific Export Price (lag1) Plus Pacific Freight Rate (lag 2), DNS, $/Metric Ton
-30
-20
-10
0
10
20
30
40
Date
$/M
etr
ic T
on
77
Trace of Logarithms of Import Price and the Pacific Export Price (lag1) Plus Pacific Freight Rate (lag 2), DNS
4.7
4.8
4.9
5
5.1
5.2
5.3
5.4
5.5
5.6
Apr-75 Aug-76 Jan-78 May-79 Oct-80 Feb-82
Date
ln
lndnsj
lndnspjt
88
Log of Ratio of Import Price to the Sum of the Pacific Export Price (lag1) Plus Pacific Freight (lag 2), DNS
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
Date
ln
99
0
2
4
6
8
10
12
-0.10 -0.05 0.00 0.05 0.10 0.15
Series: LNRATIODNSPJTSample 1975:11 1981:10Observations 72
Mean -0.002541Median -0.001870Maximum 0.168084Minimum -0.103687Std. Dev. 0.046206Skewness 0.612068Kurtosis 5.041199
Jarque-Bera 16.99500Probability 0.000204
Log of Ratio of Import Price to the Sum of pacific Export Price (lag1) Plus Pacific Freight (lag 2), DNS
1010
1111
1212
1313
1414
1515
1616
1717
0
2
4
6
8
10
12
-0.10 -0.05 0.00 0.05 0.10
Series: ResidualsSample 1975:12 1981:10Observations 71
Mean 4.47E-15Median -0.002010Maximum 0.123133Minimum -0.095299Std. Dev. 0.038372Skewness 0.409841Kurtosis 4.159879
Jarque-Bera 5.967543Probability 0.050602
Residulas from ARONE Model for lnratiodnspjt
1818
Error Correction VAR, One LagError Correction VAR, One Lag
1919
VEC Cont.VEC Cont.
2020
Johansen Summary TableJohansen Summary Table
2121
Johansen Test: No Data Trend, InterceptJohansen Test: No Data Trend, Intercept
2222
Impulse Response FunctionsImpulse Response FunctionsOrder: lndnsj, lndnspjtOrder: lndnsj, lndnspjt
-0.02
0.00
0.02
0.04
0.06
0.08
1 2 3 4 5 6 7 8 9 10
Response of LNDNSJ to LNDNSJ
-0.02
0.00
0.02
0.04
0.06
0.08
1 2 3 4 5 6 7 8 9 10
Response of LNDNSJ to LNDNSPJT
-0.02
0.00
0.02
0.04
0.06
0.08
1 2 3 4 5 6 7 8 9 10
Response of LNDNSPJT to LNDNSJ
-0.02
0.00
0.02
0.04
0.06
0.08
1 2 3 4 5 6 7 8 9 10
Response of LNDNSPJT to LNDNSPJT
Response to One S.D. Innovations ± 2 S.E.
2323
Impulse Response FunctionsImpulse Response FunctionsOrder: lndnspjt, lndnsjOrder: lndnspjt, lndnsj
-0.02
0.00
0.02
0.04
0.06
0.08
1 2 3 4 5 6 7 8 9 10
Response of LNDNSJ to LNDNSJ
-0.02
0.00
0.02
0.04
0.06
0.08
1 2 3 4 5 6 7 8 9 10
Response of LNDNSJ to LNDNSPJT
-0.02
0.00
0.02
0.04
0.06
0.08
1 2 3 4 5 6 7 8 9 10
Response of LNDNSPJT to LNDNSJ
-0.02
0.00
0.02
0.04
0.06
0.08
1 2 3 4 5 6 7 8 9 10
Response of LNDNSPJT to LNDNSPJT
Response to One S.D. Innovations ± 2 S.E.
2424
Variance DecompositionVariance DecompositionOrder: lndnsj, lndnspjtOrder: lndnsj, lndnspjt
2525
Table Three: Gulf DNS Table Three: Gulf DNS Log of Ratio of Import Price to Gulf Export Price Log of Ratio of Import Price to Gulf Export Price
(lag 1) Plus Gulf Freight (lag2)(lag 1) Plus Gulf Freight (lag2) StationaryStationary
No unit rootNo unit root AR (1) Model: root 0.63, normal residualAR (1) Model: root 0.63, normal residual
Log of Import Price and Log of Gulf Import Price Log of Import Price and Log of Gulf Import Price (lag 1) Plus Gulf Freight (lag 2)(lag 1) Plus Gulf Freight (lag 2) CointegratedCointegrated
VEC: One lagVEC: One lag Rank: 0, 0, 1, 0, 2Rank: 0, 0, 1, 0, 2 Linear trend in Data; Cointegration equation:Intercept, no Linear trend in Data; Cointegration equation:Intercept, no
trend, rank one, 5%trend, rank one, 5%
2626
Trace of Import Price and Gulf Export Price (lagged one) Plus Gulf Freight Rate (lagged two), DNS, $/ Metric Ton
0
50
100
150
200
250
300
Date
$/M
etr
ic T
on
dnsj
dnsgjt
2727
Trace: Import Price Minus the Sum of Export Price (lagged one) Plus the Freight Rate (lagged two), DNS, $/Metric Ton, Pacific Vs. Gulf
-30
-20
-10
0
10
20
30
40
Date
$/M
etr
ic T
on
Pacific
Gulf
2828
Trace: Import Price Minus the Sum of the Gulf Export Price (lagged one) Plus Gulf Freight Rate (lagged two), DNS, $/Metric Ton
-30
-20
-10
0
10
20
30
40
Date
$/M
etr
ic T
on
2929
Logarithms of Import Price and Sum of Gulf Export Price (lagged one) Plus Gulf Freight Rate (lagged two), DNS
4.2
4.4
4.6
4.8
5
5.2
5.4
5.6
5.8
Date
ln
lndnsj
lndnsgjt
3030
Log of Ratio of Import Price to the Sum of the Gulf Export Price (lagged one) Plus the Gulf Freight Rate (lagged two), DNS
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
Date
ln
3131
0
2
4
6
8
-0.10 -0.05 0.00 0.05 0.10 0.15
Series: LNRATIODNSGJTSample 1975:11 1981:10Observations 72
Mean 0.001363Median -0.011442Maximum 0.168586Minimum -0.102988Std. Dev. 0.056302Skewness 0.595124Kurtosis 3.082605
Jarque-Bera 4.270544Probability 0.118212
Log of Ratio of Import Price to the Sum of the Gulf Export Price (lag 1) Plus Gulf Freight (lag 2), DNS
3232
3333
3434
3535
3636
3737
3838
0
2
4
6
8
10
-0.10 -0.05 0.00 0.05 0.10
Series: ResidualsSample 1975:12 1981:10Observations 71
Mean 4.53E-15Median -0.006443Maximum 0.114451Minimum -0.106399Std. Dev. 0.043963Skewness 0.705771Kurtosis 3.568447
Jarque-Bera 6.850271Probability 0.032545
Residuals from ARONE Model for LNRATIODNSGJT
3939
Johansen Test SummaryJohansen Test Summary
4040
Error Correction ModelError Correction Model
4141
VEC Cont.VEC Cont.
4242
Johansen TestJohansen Test
4343
Impulse Response FunctionsImpulse Response FunctionsOrder: lndnsj, lndnsgjtOrder: lndnsj, lndnsgjt
-0.04
-0.02
0.00
0.02
0.04
0.06
1 2 3 4 5 6 7 8 9 10
Response of LNDNSJ to LNDNSJ
-0.04
-0.02
0.00
0.02
0.04
0.06
1 2 3 4 5 6 7 8 9 10
Response of LNDNSJ to LNDNSGJT
-0.04
-0.02
0.00
0.02
0.04
0.06
1 2 3 4 5 6 7 8 9 10
Response of LNDNSGJT to LNDNSJ
-0.04
-0.02
0.00
0.02
0.04
0.06
1 2 3 4 5 6 7 8 9 10
Response of LNDNSGJT to LNDNSGJT
Response to One S.D. Innovations ± 2 S.E.
4444
Impulse Response FunctionsImpulse Response FunctionsOrder: lndnsgjt, lndnsjOrder: lndnsgjt, lndnsj
-0.02
0.00
0.02
0.04
0.06
0.08
1 2 3 4 5 6 7 8 9 10
Response of LNDNSJ to LNDNSJ
-0.02
0.00
0.02
0.04
0.06
0.08
1 2 3 4 5 6 7 8 9 10
Response of LNDNSJ to LNDNSGJT
-0.02
0.00
0.02
0.04
0.06
1 2 3 4 5 6 7 8 9 10
Response of LNDNSGJT to LNDNSJ
-0.02
0.00
0.02
0.04
0.06
1 2 3 4 5 6 7 8 9 10
Response of LNDNSGJT to LNDNSGJT
Response to One S.D. Innovations ± 2 S.E.
4545
Variance DecompositionVariance DecompositionOrder: lndnsj, lndnsgjtOrder: lndnsj, lndnsgjt
4646
Table Four: Pacific DNSTable Four: Pacific DNSLog of Ratio of Import Price to Pacific Log of Ratio of Import Price to Pacific
Export Price (lag 1), No Pacific Freight Export Price (lag 1), No Pacific Freight StationaryStationary
Unit root ?Unit root ?ARONE Model, root = 0.73, normal residualARONE Model, root = 0.73, normal residual
Log of Import Price and Log of Pacific Log of Import Price and Log of Pacific Export Price (lag 1), No Pacific Freight Export Price (lag 1), No Pacific Freight Not cointegratedNot cointegrated
VEC 1 lagVEC 1 lagRank: 0, 0, 0, 0, 0Rank: 0, 0, 0, 0, 0
4747
Trace of Import Price And Pacific Export Price (lagged one), DNS
0
50
100
150
200
250
300
Year
$/M
etr
ic T
on
DNSJ
DNSP
4848
Export Price Minus Pacific Export Price (lagged one), No Freight, DNS
-10
0
10
20
30
40
50
60
Date
$/M
etr
ic T
on
4949
Trace of Logarithms of Import Price and Pacific Export Price (one lag), No Freight, DNS
4.2
4.4
4.6
4.8
5
5.2
5.4
5.6
Date
ln
lndns
lndnspj
5050
Logarithm of Ratio of Import Price to Pacific Export Price (lag one), No Freight, DNS
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
Date
lnR
ati
o
5151
0
2
4
6
8
0.00 0.05 0.10 0.15 0.20 0.25
Series: LNRATIODNSPJSample 1975:10 1981:10Observations 73
Mean 0.111239Median 0.108041Maximum 0.275182Minimum -0.022728Std. Dev. 0.058990Skewness 0.184024Kurtosis 3.067675
Jarque-Bera 0.425954Probability 0.808175
Logarithm of Ratio of Import Price to Export Price (lag1) No Freight, DNS
5252
5353
5454
5555
5656
5757
5858
5959
6060
6161
0
2
4
6
8
10
12
-0.10 -0.05 0.00 0.05 0.10
Series: ResidualsSample 1975:11 1981:10Observations 72
Mean 1.16E-14Median -0.002773Maximum 0.106137Minimum -0.102300Std. Dev. 0.042146Skewness 0.184677Kurtosis 3.423791
Jarque-Bera 0.948062Probability 0.622488
Residuals from ARONE Model of lnratiodnspj
6262
Johansen Summary TableJohansen Summary Table
6363
Table Four: Gulf DNSTable Four: Gulf DNSLog of Ratio of Import Price to Gulf Export Log of Ratio of Import Price to Gulf Export
Price (lag 1), No Gulf Freight Price (lag 1), No Gulf Freight StationaryStationary
Unit root ?Unit root ?ARONE Model, root = 0.74, normal residualARONE Model, root = 0.74, normal residual
Log of Import Price and Log of Gulf Import Log of Import Price and Log of Gulf Import Price (lag 1), No Gulf Freight Price (lag 1), No Gulf Freight Not cointegratedNot cointegrated
VEC lag 1VEC lag 1Rank: 0, 0, 0, 0, 2Rank: 0, 0, 0, 0, 2
6464
Trace of Import Price and Gulf Export Price (lagged one), No Freight, DNS
0
50
100
150
200
250
300
Date
$/M
etr
ic T
on
dnsj
dnsgj
6565
Import Price Minus Export Price (lagged one), No Freight, DNS, Pacific Vs. Gulf
-10
0
10
20
30
40
50
60
70
Date
$/M
etr
ic T
on
Pacific
Gulf
6666
Logarithms of Import Price and Gulf Export Price (lagged one), No Freight, DNS
4
4.2
4.4
4.6
4.8
5
5.2
5.4
5.6
Date
ln
lndnsj
lndnsgj
6767
Logarithm of Ratio of Export Price to Import Price (lagged one), No Freight, DNS, Pacific Vs. Gulf
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Date
lnR
ati
o
Pacif ic
Gulf
6868
0
2
4
6
8
10
12
14
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Series: LNRATIODNSGJSample 1975:10 1981:10Observations 73
Mean 0.138111Median 0.129912Maximum 0.321584Minimum 0.007117Std. Dev. 0.075268Skewness 0.349590Kurtosis 2.448129
Jarque-Bera 2.413303Probability 0.299198
Logarithm of Ratio of Import Price to Gulf Export Price (lag1), No Freight, DNS
6969
7070
7171
7272
7373
7474
7575
7676
7777
7878
0
2
4
6
8
10
-0.10 -0.05 0.00 0.05 0.10
Series: ResidualsSample 1975:11 1981:10Observations 72
Mean 8.38E-15Median -0.002408Maximum 0.134577Minimum -0.112497Std. Dev. 0.050955Skewness 0.631458Kurtosis 3.463806
Jarque-Bera 5.430217Probability 0.066198
Residuals from ARONE Model of lnratiodnsgj
7979
Johansen Summary TableJohansen Summary Table
8080
Table Three: Gulf Hard WinterTable Three: Gulf Hard Winter Log of Ratio of Import Price to Gulf Export Price Log of Ratio of Import Price to Gulf Export Price
(lag 1) Plus Gulf Freight (lag2)(lag 1) Plus Gulf Freight (lag2) StationaryStationary
No unit rootNo unit root ARONE (1) Model: root 0.39, normal residualARONE (1) Model: root 0.39, normal residual
Log of Import Price and Log of Pacific Import Log of Import Price and Log of Pacific Import Price (lag 1) Plus Pacific Freight (lag 2)Price (lag 1) Plus Pacific Freight (lag 2) CointegratedCointegrated
VEC one lagVEC one lag Rank: 1, 1, 1, 1, 1Rank: 1, 1, 1, 1, 1 No Intercept, no trend, rank oneNo Intercept, no trend, rank one
8181
Trace of Import Price and Gulf Export Price (lagged one) Plus Gulf Freight (lagged two), Hard Winter 13%
0
50
100
150
200
250
300
Date
$/M
etr
ic t
on
hw j
hw gjy
8282
Hard Winter 13 %: Import Price Minus Gulf Export Price (lagged one) Minus Gulf Freight (lagged two)
-20
-10
0
10
20
30
40
Date
$/M
etr
ic T
on
8383
Hard Winter 13%: Logarithms of Import Price and Gulf Export Price (lagged one) Plus Freight (lagged two)
4.2
4.4
4.6
4.8
5
5.2
5.4
5.6
Date
ln
lnhwj
lnhwgjt
8484
Hard Winter 13%: Logarithm of Ratio of Import Price to Gulf Export Price (lagged one) Plus Gulf Freight (lagged two)
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
Date
lnR
ati
o
8585
0
2
4
6
8
10
12
-0.10 -0.05 0.00 0.05 0.10 0.15
Series: LNRATIOHWGJTSample 1975:11 1981:10Observations 72
Mean 0.029073Median 0.022096Maximum 0.176761Minimum -0.090754Std. Dev. 0.046900Skewness 0.605364Kurtosis 3.877209
Jarque-Bera 6.706075Probability 0.034978
Logarithm of Ratio of Import Price to Sum of Gulf Export Price (lag 1) Plus Gulf Freight (lag 2), Hard Winter
8686
8787
8888
8989
9090
9191
9292
0
2
4
6
8
10
-0.10 -0.05 0.00 0.05 0.10
Series: ResidualsSample 1975:12 1981:10Observations 71
Mean 1.15E-15Median -0.004257Maximum 0.113639Minimum -0.127967Std. Dev. 0.042971Skewness 0.082877Kurtosis 3.528246
Jarque-Bera 0.906782Probability 0.635470
Residuals from ARONE Model for lnratiohwgjt
9393
Johansen Summary TableJohansen Summary Table
9494
Johansen TestJohansen Test
9595
Error Correction ModelError Correction Model
Determinant Residual Covariance: 1.12 E-06 Log Likelihood: 280.8788 Akaike Information Criteria: -7.7965 Schwarz Criteria: -7.9356
9696
VEC Cont. VEC Cont.
9797
Impulse Response FunctionsImpulse Response FunctionsOrder: lnhwj, lnhwgjtOrder: lnhwj, lnhwgjt
-0.02
0.00
0.02
0.04
0.06
0.08
1 2 3 4 5 6 7 8 9 10
Response of LNHWJ to LNHWJ
-0.02
0.00
0.02
0.04
0.06
0.08
1 2 3 4 5 6 7 8 9 10
Response of LNHWJ to LNHWGJT
-0.02
0.00
0.02
0.04
0.06
0.08
1 2 3 4 5 6 7 8 9 10
Response of LNHWGJT to LNHWJ
-0.02
0.00
0.02
0.04
0.06
0.08
1 2 3 4 5 6 7 8 9 10
Response of LNHWGJT to LNHWGJT
Response to One S.D. Innovations ± 2 S.E.
9898
Impulse Response FunctionsImpulse Response FunctionsOrder: lnhwgjt, lnhwjOrder: lnhwgjt, lnhwj
-0.02
0.00
0.02
0.04
0.06
0.08
1 2 3 4 5 6 7 8 9 10
Response of LNHWJ to LNHWJ
-0.02
0.00
0.02
0.04
0.06
0.08
1 2 3 4 5 6 7 8 9 10
Response of LNHWJ to LNHWGJT
-0.02
0.00
0.02
0.04
0.06
0.08
1 2 3 4 5 6 7 8 9 10
Response of LNHWGJT to LNHWJ
-0.02
0.00
0.02
0.04
0.06
0.08
1 2 3 4 5 6 7 8 9 10
Response of LNHWGJT to LNHWGJT
Response to One S.D. Innovations ± 2 S.E.
9999
Variance DecompositionVariance DecompositionOrder: lnhwj, lnhwgjtOrder: lnhwj, lnhwgjt
100100
Table Four: Gulf HWTable Four: Gulf HWLog of Ratio of Import Price to Gulf Export Log of Ratio of Import Price to Gulf Export
Price (lag 1), No Freight Price (lag 1), No Freight StationaryStationary
No unit root ?No unit root ?ARONE Model, root 0.64, normal residualARONE Model, root 0.64, normal residual
Log of Import Price and Log of Gulf Export Log of Import Price and Log of Gulf Export Price (lag 1), No Freight Price (lag 1), No Freight Probably Not CointegratedProbably Not Cointegrated
Rank zero except for VAR with linear trend in data, Rank zero except for VAR with linear trend in data, intercept and no trend in cointegrating equation, intercept and no trend in cointegrating equation, rank one, significant at 5% levelrank one, significant at 5% level
101101
Traces: #2 Hard Winter 13% Import Price and Gulf Export Price (lagged one); No Freight
0
50
100
150
200
250
300
Date
$/M
etr
ic T
on
HWJ
HWGJ
102102
Trace: #2 Hard Winter 13% Import Price Minus Gulf Export Price (lagged one); No Freight
0
10
20
30
40
50
60
70
Date
$/M
etr
ic T
on
103103
Traces: Logarithms of #2 Hard Winter 13% Import Price and Gulf Export Price (lagged one); No Freight
0
1
2
3
4
5
6
Dtae
ln
lnhwj
lnhwgj
104104
Trace: #2 Hard Winter 13%, Logarithm of Ratio of Import Price to the Gulf Export Price (lagged one); No Freight
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Apr-75 Aug-76 Jan-78 May-79 Oct-80 Feb-82
Date
lnR
ati
o
105105
0
5
10
15
20
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35
Series: LNRATIOHWGJSample 1975:10 1981:10Observations 73
Mean 0.174924Median 0.164303Maximum 0.329599Minimum 0.000000Std. Dev. 0.066093Skewness 0.182238Kurtosis 2.951501
Jarque-Bera 0.411220Probability 0.814151
#2 Hard Winter 13%, Logarithm of Ratio of Import Price to Gulf Export Price (lag1); No Freight
106106
107107
108108
109109
110110
111111
112112
113113
114114
115115
0
2
4
6
8
10
12
-0.15 -0.10 -0.05 0.00 0.05 0.10
Series: ResidualsSample 1975:11 1981:10Observations 72
Mean 4.68E-15Median 0.004261Maximum 0.108886Minimum -0.152458Std. Dev. 0.051044Skewness -0.254955Kurtosis 3.327365
Jarque-Bera 1.101525Probability 0.576510
#2 Hard Winter 13%: Residuals from ARONE Model of lnratiogj
116116
Johansen Summary TableJohansen Summary Table
117117
Error Correction ModelError Correction Model
118118
VEC Cont.VEC Cont.
119119
Johansen TestJohansen Test
120120
Impulse Response FunctionsImpulse Response FunctionsOrder: lnhwj, lnhwgjOrder: lnhwj, lnhwgj
-0.02
0.00
0.02
0.04
0.06
1 2 3 4 5 6 7 8 9 10
Response of LNHWJ to LNHWJ
-0.02
0.00
0.02
0.04
0.06
1 2 3 4 5 6 7 8 9 10
Response of LNHWJ to LNHWGJ
-0.02
-0.01
0.00
0.01
0.02
0.03
0.04
0.05
1 2 3 4 5 6 7 8 9 10
Response of LNHWGJ to LNHWJ
-0.02
-0.01
0.00
0.01
0.02
0.03
0.04
0.05
1 2 3 4 5 6 7 8 9 10
Response of LNHWGJ to LNHWGJ
Response to One S.D. Innovations
121121
Impulse Response FunctionsImpulse Response FunctionsOrder: lnhwgj, lnhwjOrder: lnhwgj, lnhwj
-0.02
0.00
0.02
0.04
0.06
1 2 3 4 5 6 7 8 9 10
Response of LNHWJ to LNHWJ
-0.02
0.00
0.02
0.04
0.06
1 2 3 4 5 6 7 8 9 10
Response of LNHWJ to LNHWGJ
-0.01
0.00
0.01
0.02
0.03
0.04
0.05
1 2 3 4 5 6 7 8 9 10
Response of LNHWGJ to LNHWJ
-0.01
0.00
0.01
0.02
0.03
0.04
0.05
1 2 3 4 5 6 7 8 9 10
Response of LNHWGJ to LNHWGJ
Response to One S.D. Innovations
122122
Variance DecompositionVariance DecompositionOrder: lnhwj, lnhwgjOrder: lnhwj, lnhwgj
123123
Table Three: Pacific WWTable Three: Pacific WW Log of Ratio of Import Price to Pacific Export Log of Ratio of Import Price to Pacific Export
Price (lag 1) Plus Pacific Freight (lag2)Price (lag 1) Plus Pacific Freight (lag2) StationaryStationary
No unit rootNo unit root ARONE Model, root 0.49, normal residualARONE Model, root 0.49, normal residual
Log of Import Price and Log of Pacific Import Log of Import Price and Log of Pacific Import Price (lag 1) Plus Pacific Freight (lag 2)Price (lag 1) Plus Pacific Freight (lag 2) CointegratedCointegrated
VEC: one lagVEC: one lag Rank: 1, 1, 1 ,1 , 2Rank: 1, 1, 1 ,1 , 2 Data: No Trend; integrating equation: Intercept, no trend, Data: No Trend; integrating equation: Intercept, no trend,
rank one 1%rank one 1%
124124
Western White Import Price and Pacific Export Price (lagged One) Plus Pacific Freight (lagged two)
0
50
100
150
200
250
Date
$/M
etr
ic T
on
wwj
wwpjt
125125
Western White: Import Price Minus Pacific Export Price (lagged one) Minus Pacific Freight Price (lagged two)
-15
-10
-5
0
5
10
15
20
25
30
Date
$/ M
etr
ic T
on
126126
Western White: Logarithms of Import Price and Pacific export Price (lagged one) Plus Pacific Freight Rate (lagged two)
0
1
2
3
4
5
6
Date
ln
lnwwj
lnwwpjt
127127
Western White: Log of Ratio of Import Price to Pacific Export Price (lagged one) Plus Pacific Freight Rate (lagged two)
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
Date
ln
128128
0
2
4
6
8
10
-0.10 -0.05 0.00 0.05 0.10 0.15
Series: LNRATIOPJTSample 1975:11 1981:10Observations 72
Mean 0.001351Median 0.003264Maximum 0.155533Minimum -0.101944Std. Dev. 0.043530Skewness 0.478942Kurtosis 4.886777
Jarque-Bera 13.43241Probability 0.001211
Western White: Log of Ratio of Import Price to Pacific Export Price (lag1) Plus Pacific Freight (lag2)
129129
130130
131131
132132
133133
134134
135135
136136
0
2
4
6
8
10
-0.10 -0.05 0.00 0.05 0.10
Series: ResidualsSample 1975:12 1981:10Observations 71
Mean 3.04E-15Median 0.000236Maximum 0.124251Minimum -0.090719Std. Dev. 0.038017Skewness 0.024306Kurtosis 3.713539
Jarque-Bera 1.513192Probability 0.469261
Residuals from ARONE Model for lnratiowwpjt
137137
Johansen Summary TableJohansen Summary Table
138138
Error Correction ModelError Correction Model
139139
Johansen TestJohansen Test
140140
Impulse Response FunctionsImpulse Response FunctionsOrdering: lnwwj lnwwpjtOrdering: lnwwj lnwwpjt
-0.02
0.00
0.02
0.04
0.06
0.08
1 2 3 4 5 6 7 8 9 10
Response of LNWWJ to LNWWJ
-0.02
0.00
0.02
0.04
0.06
0.08
1 2 3 4 5 6 7 8 9 10
Response of LNWWJ to LNWWPJT
-0.02
0.00
0.02
0.04
0.06
0.08
1 2 3 4 5 6 7 8 9 10
Response of LNWWPJT to LNWWJ
-0.02
0.00
0.02
0.04
0.06
0.08
1 2 3 4 5 6 7 8 9 10
Response of LNWWPJT to LNWWPJT
Response to One S.D. Innovations ± 2 S.E.
141141
Impulse Response FunctionsImpulse Response FunctionsOrdering: lnwwpjt lnwwjOrdering: lnwwpjt lnwwj
-0.02
0.00
0.02
0.04
0.06
0.08
1 2 3 4 5 6 7 8 9 10
Response of LNWWJ to LNWWJ
-0.02
0.00
0.02
0.04
0.06
0.08
1 2 3 4 5 6 7 8 9 10
Response of LNWWJ to LNWWPJT
-0.02
0.00
0.02
0.04
0.06
0.08
1 2 3 4 5 6 7 8 9 10
Response of LNWWPJT to LNWWJ
-0.02
0.00
0.02
0.04
0.06
0.08
1 2 3 4 5 6 7 8 9 10
Response of LNWWPJT to LNWWPJT
Response to One S.D. Innovations ± 2 S.E.
142142
Variance DecompositionVariance DecompositionOrdering: lnwwj lnwwpjtOrdering: lnwwj lnwwpjt
143143
Table Four: Pacific WWTable Four: Pacific WWLog of Ratio of Import Price to Pacific Log of Ratio of Import Price to Pacific
Export Price (lag 1), No Freight Export Price (lag 1), No Freight StationaryStationary
No unit root ?No unit root ?ARONE Model, root 0.73, normal residualARONE Model, root 0.73, normal residual
Log of Import Price and Log of Pacific Log of Import Price and Log of Pacific Export Price (lag 1), No Freight Export Price (lag 1), No Freight Probably Not CointegratedProbably Not Cointegrated
Rank zero except for VAR with linear trend in data, Rank zero except for VAR with linear trend in data, intercept and no trend in cointegrating equation, intercept and no trend in cointegrating equation, rank one, significant at 5% levelrank one, significant at 5% level
144144
Trace: Import Price anf Export Price (lagged one), No Freight, Western White
0
50
100
150
200
250
Date
$/M
etr
ic T
on
WWJ
WWPJ
145145
Trace: Import Price Minus Pacific Export Price (lagged one), No Freight, Western White
0
5
10
15
20
25
30
35
40
45
50
Date
$/M
etr
ic T
on
146146
Trace: Logarithms of Import Price and Pacific Export Price (lagged one), No Freight, Western White
4.2
4.4
4.6
4.8
5
5.2
5.4
5.6
Date
ln
lnwwj
lnwwpj
147147
0.00
0.05
0.10
0.15
0.20
0.25
0.30
76 77 78 79 80 81
LNRATIOWWPJ
Log of Ratio of Import Price to Pacific Export Price (lag1), Western White
148148
149149
150150
151151
152152
153153
154154
155155
156156
Johansen Summary TableJohansen Summary Table
157157
Table 3: log ratio of Import Price/ Table 3: log ratio of Import Price/ [Export Price (lag 1) + Freight (lag 2)][Export Price (lag 1) + Freight (lag 2)]
DNSGJTDNSGJT DNSPJTDNSPJT WWPJTWWPJT HWGJTHWGJT
AR(1)AR(1) 0.630.63 0.540.54 0.490.49 0.390.39
MA(1)MA(1) 00 00 00 00
Model ResModel Res normalnormal normalnormal normalnormal normalnormal
VECVEC 1 lag1 lag 1 lag1 lag 1 lag1 lag 1 lag1 lag
5 Mod. rank5 Mod. rank 0,0,0,0,11,0,2,0,2 1,1,11,1,1,2,1,1,2 1,1,11,1,1,2,1,1,2 1,1,1,1,11,1,1,1,1
Rank 1Rank 1 5%5% 1% (3/4)1% (3/4) 1% (3/4)1% (3/4) 1% all1% all
158158
Table 4: log ratio of Import Price/ Table 4: log ratio of Import Price/ [Export Price (lag 1)][Export Price (lag 1)]
DNSGJDNSGJ DNSPJDNSPJ WWPJWWPJ HWGJHWGJ
AR(1)AR(1) 0.740.74 0.710.71 0.730.73 0.640.64
MA(1)MA(1) 00 00 00 00
Model ResModel Res normalnormal normalnormal normalnormal normalnormal
VECVEC 1 lag1 lag 1 lag1 lag 1 lag1 lag 1 lag1 lag
5 Mod. rank5 Mod. rank 0,0,0,0,20,0,0,0,2 0,0,0,0,00,0,0,0,0 0,0,0,0,00,0,0,0,0 0,0,0,0,11,0,2,0,2
Rank 1Rank 1 5% 5%
159159
Table 4: log ratio of Import Price/ Table 4: log ratio of Import Price/ [Export Price (lag 1) ] No Freight[Export Price (lag 1) ] No Freight
AR(1)AR(1) MA(1)MA(1) Model Res.Model Res. JohansenJohansen
DNSGJDNSGJ 0.740.74 00 NormalNormal rank 0* rank 0*
DNSPJDNSPJ 0.710.71 00 NormalNormal rank 0 rank 0
WWPJWWPJ 0.720.72 00 NormalNormal rank 0rank 0
HWGJHWGJ 0.640.64 00 NormalNormal rank 0* (5%)#rank 0* (5%)#
•Rank 2 for model: quadratic trend in data, cointegrating equation: intercept, trend•#Rank 1 for model: linear trend in data, cointegrating equation: intercept, no trend
160160
Table 5: log ratio of Import Price/ Table 5: log ratio of Import Price/ [Export Price ( no lag ) + Freight (lag1)][Export Price ( no lag ) + Freight (lag1)]
AR(1)AR(1) MA(j)MA(j) model res.model res. JohansenJohansen
DNSGJTDNSGJT 0.760.76 -.68 (4)-.68 (4) NormalNormal Rank 1* (5%)Rank 1* (5%)
DNSPJTDNSPJT 0.920.92 0 arch 10 arch 1 kurtotickurtotic Rank 0 Rank 0
WWPJTWWPJT 0.730.73 00 NormalNormal Rank 1* (1%)Rank 1* (1%)
HWGJTHWGJT 0.530.53 -.33 (6)-.33 (6) kurtotickurtotic Rank 1* (5%)Rank 1* (5%)
* Rank 2 for model: quadratic trend in data, cointegrating equation: intercept, trend
161161
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