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Full sample analysis:
CATS for RATS version 2 - 12/14/2006 11:29
MODEL SUMMARY
Sample: 1960:02 to 2002:01 (168 observations)
Effective Sample: 1960:04 to 2002:01 (166 observations)
Obs. - No. of variables: 150
System variables: LY LC LH LKP
Shift-dummy series: C(1978:01)
Dummy-series: DUMP7004{0} DUMP7403{0} DUMP7404{0} DUMTR8001{0}
Constant/Trend: Restricted Trend
Lags in VAR: 2
The unrestricted estimates:
BETA(transposed)
LY LC LH LKP C(1978:01) TREND
Beta(1) 216.92 -164.41 -10.79 -39.23 1.71 -0.06
Beta(2) 72.25 -79.07 -6.44 -17.68 -2.54 0.15
Beta(3) 28.47 20.10 -29.95 -11.14 2.01 -0.15
Beta(4) 1.94 23.39 32.49 -17.98 1.58 -0.05
ALPHA
Alpha(1) Alpha(2) Alpha(3) Alpha(4)
DLY -0.00 0.00 -0.00 -0.00
(-5.77) (4.02) (-0.30) (-0.61)
DLC -0.00 0.00 -0.00 -0.00
(-0.60) (2.87) (-1.20) (-1.43)
DLH -0.00 0.00 0.00 -0.00
(-2.74) (2.03) (2.19) (-1.05)
DLKP 0.00 0.00 0.00 0.00
(3.10) (4.17) (0.65) (0.99)
PI
LY LC LH LKP C(1978:01) TREND
DLY -0.52 0.33 0.01 0.09 -0.01 0.00
(-4.22) (3.30) (0.56) (3.54) (-5.43) (4.56)
DLC 0.02 -0.08 -0.01 0.01 -0.01 0.00
(0.17) (-1.00) (-0.49) (0.25) (-3.26) (3.18)
DLH -0.12 0.10 -0.03 0.02 -0.00 0.00
(-1.68) (1.67) (-1.81) (1.38) (-1.78) (0.88)
DLKP 0.91 -0.73 -0.04 -0.20 -0.00 0.00
(4.31) (-4.34) (-1.04) (-4.60) (-0.60) (1.18)
Log-Likelihood = 3436.87
RE-NORMALIZATION OF THE EIGENVECTORS:
THE EIGENVECTOR(s)(transposed)
LY LC LH LKP C(1978:01) TREND
Beta(1) 216.92 -164.41 -10.79 -39.23 1.71 -0.06
Beta(2) 72.25 -79.07 -6.44 -17.68 -2.54 0.15
THE MATRICES BASED ON 2 COINTEGRATING VECTORS:
BETA(transposed)
LY LC LH LKP C(1978:01) TREND
Beta(1) 1.00 -0.76 -0.05 -0.18 0.01 -0.00
Beta(2) -0.91 1.00 0.08 0.22 0.03 -0.00
ALPHA
Alpha(1) Alpha(2)
DLY -0.67 -0.17
(-5.77) (-4.02)
DLC -0.06 -0.10
(-0.60) (-2.84)
DLH -0.19 -0.05
(-2.69) (-1.99)
DLKP 0.62 -0.30
(3.09) (-4.15)
PI
LY LC LH LKP C(1978:01) TREND
DLY -0.52 0.34 0.02 0.08 -0.01 0.00
(-4.20) (3.46) (2.89) (3.61) (-6.55) (5.95)
DLC 0.03 -0.06 -0.01 -0.01 -0.00 0.00
(0.33) (-0.70) (-0.95) (-0.63) (-2.69) (2.85)
DLH -0.14 0.09 0.01 0.02 -0.00 0.00
(-1.92) (1.56) (1.29) (1.64) (-3.16) (2.89)
DLKP 0.89 -0.77 -0.06 -0.18 -0.00 0.00
(4.24) (-4.58) (-4.78) (-4.52) (-1.72) (2.61)
Log-Likelihood = 3430.20
TEST OF RESTRICTED MODEL: CHISQR(3) = 19.84 [0.00]
RE-NORMALIZATION OF THE EIGENVECTORS:
THE EIGENVECTOR(s)(transposed)
LY LC LH LKP C(1978:01) TREND
Beta(1) 47.79 0.00 -37.27 -10.51 0.00 -0.13
Beta(2) 204.00 -165.18 0.00 -36.31 1.70 -0.02
THE MATRICES BASED ON 2 COINTEGRATING VECTORS:
BETA(transposed)
LY LC LH LKP C(1978:01) TREND
Beta(1) 1.00 0.00 -0.78 -0.22 0.00 -0.00
(.NA) (.NA) (.NA) (.NA) (.NA) (-17.24)
Beta(2) -1.24 1.00 0.00 0.22 -0.01 0.00
(-30.00) (.NA) (.NA) (12.83) (-3.18) (1.11)
ALPHA
Alpha(1) Alpha(2)
DLY -0.04 0.51
(-1.55) (5.49)
DLC -0.02 0.04
(-0.75) (0.52)
DLH 0.02 0.15
(1.31) (2.92)
DLKP 0.06 -0.46
(1.36) (-2.86)
PI
LY LC LH LKP C(1978:01) TREND
DLY -0.67 0.51 0.03 0.12 -0.01 0.00
(-5.47) (5.49) (1.55) (5.43) (-5.49) (2.46)
DLC -0.06 0.04 0.01 0.01 -0.00 0.00
(-0.65) (0.52) (0.75) (0.67) (-0.52) (0.81)
DLH -0.17 0.15 -0.02 0.03 -0.00 -0.00
(-2.44) (2.92) (-1.31) (2.33) (-2.92) (-0.72)
DLKP 0.63 -0.46 -0.05 -0.11 0.00 -0.00
(2.97) (-2.86) (-1.36) (-2.98) (2.86) (-1.81)
Log-Likelihood = 3420.28
TEST OF RESTRICTED MODEL: CHISQR(3) = 19.8354 [0.0002]
RE-NORMALIZATION OF THE EIGENVECTORS:
THE EIGENVECTOR(s)(transposed)
LY LC LH LKP C(1978:01) TREND
Beta(1) 47.7867 0.0000 -37.2737 -10.5131 0.0000 -0.1311
Beta(2) 204.0047 -165.1841 0.0000 -36.3104 1.7032 -0.0248
THE MATRICES BASED ON 2 COINTEGRATING VECTORS:
BETA(transposed)
LY LC LH LKP C(1978:01) TREND
Beta(1) 1.0000 0.0000 -0.7800 -0.2200 0.0000 -0.0027
(.NA) (.NA) (.NA) (.NA) (.NA) (-17.2432)
Beta(2) -1.2350 1.0000 0.0000 0.2198 -0.0103 0.0002
(-29.9952) (.NA) (.NA) (12.8293) (-3.1824) (1.1106)
ALPHA
Alpha(1) Alpha(2)
DLY -0.0417 0.5096
(-1.5501) (5.4855)
DLC -0.0165 0.0391
(-0.7537) (0.5158)
DLH 0.0197 0.1524
(1.3065) (2.9181)
DLKP 0.0629 -0.4555
(1.3641) (-2.8593)
PI
LY LC LH LKP C(1978:01) TREND
DLY -0.6710 0.5096 0.0325 0.1212 -0.0053 0.0002
(-5.4710) (5.4855) (1.5501) (5.4343) (-5.4855) (2.4601)
DLC -0.0647 0.0391 0.0129 0.0122 -0.0004 0.0001
(-0.6476) (0.5158) (0.7537) (0.6721) (-0.5158) (0.8092)
DLH -0.1685 0.1524 -0.0154 0.0292 -0.0016 -0.0000
(-2.4435) (2.9181) (-1.3065) (2.3258) (-2.9181) (-0.7170)
DLKP 0.6254 -0.4555 -0.0490 -0.1140 0.0047 -0.0002
(2.9736) (-2.8593) (-1.3641) (-2.9800) (2.8593) (-1.8109)
Log-Likelihood = 3420.2846
RESIDUAL ANALYSIS
Residual S.E. and Cross-Correlations
DLY DLC DLH DLKP
0.0072454 0.0059061 0.0040742 0.0124249
DLY 1.0000
DLC 0.7218 1.0000
DLH 0.5659 0.3970 1.0000
DLKP 0.2531 -0.0340 0.0796 1.0000
LOG(|Sigma|) = -41.2082
Information Criteria: SC = -39.4837
H-Q = -40.1074
Trace Correlation = 0.4343
Tests for Autocorrelation
Ljung-Box(41): ChiSqr(632) = 1082.0875 [0.0000]
LM(1): ChiSqr(16) = 31.3345 [0.0122]
LM(2): ChiSqr(16) = 22.4011 [0.1307]
Test for Normality: ChiSqr(8) = 5.8557 [0.6634]
Test for ARCH:
LM(1): ChiSqr(100) = 144.3628 [0.0025]
LM(2): ChiSqr(200) = 281.1238 [0.0001]
Univariate Statistics
Mean Std.Dev Skewness Kurtosis Maximum Minimum
DLY -0.0000 0.0072 0.0667 3.7326 0.0251 -0.0194
DLC -0.0000 0.0059 0.1094 3.4147 0.0159 -0.0170
DLH -0.0000 0.0041 -0.1566 2.8812 0.0101 -0.0103
DLKP 0.0000 0.0124 -0.0751 3.4126 0.0352 -0.0389
ARCH(2) Normality R-Squared
DLY 1.1830 [0.5535] 5.3717 [0.0682] 0.5426
DLC 2.6691 [0.2633] 2.4929 [0.2875] 0.3100
DLH 10.3163 [0.0058] 0.7397 [0.6908] 0.7149
DLKP 9.0211 [0.0110] 2.4225 [0.2978] 0.7094
Second half of split sample analysis:
MODEL SUMMARY
Sample: 1981:02 to 2002:01 (84 observations)
Effective Sample: 1981:04 to 2002:01 (82 observations)
Obs. - No. of variables: 73
System variables: LY LC LH LKP
Constant/Trend: Unrestricted Constant
Lags in VAR: 2
I(2) analysis not available for the specified model.
The unrestricted estimates:
BETA(transposed)
LY LC LH LKP
Beta(1) 201.09 -165.18 -19.02 -32.32
Beta(2) -104.00 62.61 -5.29 35.12
Beta(3) -70.34 40.90 78.92 5.49
Beta(4) 26.63 0.92 -59.52 0.61
ALPHA
Alpha(1) Alpha(2) Alpha(3) Alpha(4)
DLY -0.00 0.00 -0.00 0.00
(-5.19) (0.98) (-1.91) (0.35)
DLC 0.00 0.00 -0.00 0.00
(1.21) (2.77) (-2.51) (0.03)
DLH -0.00 -0.00 -0.00 -0.00
(-4.30) (-1.78) (-2.15) (-0.28)
DLKP 0.00 -0.00 -0.00 0.00
(2.79) (-3.39) (-1.00) (0.45)
PI
LY LC LH LKP
DLY -0.56 0.47 -0.04 0.11
(-4.20) (4.64) (-0.77) (4.00)
DLC 0.06 -0.06 -0.11 0.02
(0.56) (-0.71) (-2.35) (0.92)
DLH -0.15 0.15 -0.02 0.02
(-2.25) (2.82) (-0.62) (1.34)
DLKP 1.06 -0.76 -0.15 -0.23
(4.18) (-3.94) (-1.40) (-4.46)
Log-Likelihood = 1782.37
RE-NORMALIZATION OF THE EIGENVECTORS:
THE EIGENVECTOR(s)(transposed)
LY LC LH LKP
Beta(1) 201.09 -165.18 -19.02 -32.32
Beta(2) -104.00 62.61 -5.29 35.12
THE MATRICES BASED ON 2 COINTEGRATING VECTORS:
BETA(transposed)
LY LC LH LKP
Beta(1) -1.22 1.00 0.12 0.20
Beta(2) 1.00 -0.60 0.05 -0.34
ALPHA
Alpha(1) Alpha(2)
DLY 0.48 -0.06
(5.08) (-0.96)
DLC -0.09 -0.13
(-1.17) (-2.67)
DLH 0.20 0.05
(4.18) (1.73)
DLKP -0.49 0.37
(-2.77) (3.36)
PI
LY LC LH LKP
DLY -0.64 0.51 0.05 0.11
(-4.95) (5.09) (4.63) (4.14)
DLC -0.02 -0.01 -0.02 0.03
(-0.19) (-0.15) (-1.84) (1.17)
DLH -0.19 0.17 0.03 0.02
(-2.92) (3.30) (4.50) (1.56)
DLKP 0.97 -0.71 -0.04 -0.22
(4.01) (-3.78) (-1.77) (-4.35)
Log-Likelihood = 1777.87
TEST OF RESTRICTED MODEL: CHISQR(2) = 1.44 [0.49]
RE-NORMALIZATION OF THE EIGENVECTORS:
THE EIGENVECTOR(s)(transposed)
LY LC LH LKP
Beta(1) -60.35 0.00 23.69 36.66
Beta(2) 178.27 -178.27 0.00 -12.74
THE MATRICES BASED ON 2 COINTEGRATING VECTORS:
BETA(transposed)
LY LC LH LKP
Beta(1) 1.00 0.00 -0.39 -0.61
(.NA) (.NA) (-11.26) (-17.43)
Beta(2) -1.00 1.00 0.00 0.07
(.NA) (.NA) (.NA) (10.41)
ALPHA
Alpha(1) Alpha(2)
DLY -0.11 0.50
(-3.32) (4.95)
DLC -0.03 -0.01
(-1.04) (-0.14)
DLH -0.01 0.16
(-0.65) (3.10)
DLKP 0.29 -0.75
(4.50) (-3.95)
PI
LY LC LH LKP
DLY -0.62 0.50 0.04 0.11
(-4.68) (4.95) (3.32) (3.85)
DLC -0.02 -0.01 0.01 0.02
(-0.17) (-0.14) (1.04) (0.76)
DLH -0.17 0.16 0.00 0.02
(-2.55) (3.10) (0.65) (1.32)
DLKP 1.04 -0.75 -0.11 -0.23
(4.21) (-3.95) (-4.50) (-4.49)
Log-Likelihood = 1777.15
TEST OF RESTRICTED MODEL: CHISQR(4) = 34.12 [0.00]
RE-NORMALIZATION OF THE EIGENVECTORS:
THE EIGENVECTOR(s)(transposed)
LY LC LH LKP
Beta(1) 242.70 -189.81 -22.50 -45.44
Beta(2) 13.04 22.12 -26.26 -15.69
THE MATRICES BASED ON 2 COINTEGRATING VECTORS:
BETA(transposed)
LY LC LH LKP
Beta(1) -1.28 1.00 0.12 0.24
Beta(2) -0.50 -0.84 1.00 0.60
ALPHA
Alpha(1) Alpha(2)
DLY 0.40 -0.02
(3.57) (-1.26)
DLC 0.00 0.00
(0.00) (0.00)
DLH 0.00 0.00
(0.00) (0.00)
DLKP -0.85 -0.05
(-4.43) (-1.99)
PI
LY LC LH LKP
DLY -0.50 0.41 0.03 0.08
(-3.47) (3.74) (1.40) (2.89)
DLC 0.00 0.00 0.00 0.00
(0.00) (0.00) (0.00) (0.00)
DLH 0.00 0.00 0.00 0.00
(0.00) (0.00) (0.00) (0.00)
DLKP 1.11 -0.81 -0.15 -0.23
(4.49) (-4.26) (-4.17) (-4.62)
Log-Likelihood = 1760.82
TEST OF RESTRICTED MODEL: CHISQR(2) = 5.66 [0.06]
RE-NORMALIZATION OF THE EIGENVECTORS:
THE EIGENVECTOR(s)(transposed)
LY LC LH LKP
Beta(1) 205.36 -167.92 -16.23 -34.25
Beta(2) -110.99 63.53 20.86 33.44
THE MATRICES BASED ON 2 COINTEGRATING VECTORS:
BETA(transposed)
LY LC LH LKP
Beta(1) -1.22 1.00 0.10 0.20
Beta(2) -5.32 3.05 1.00 1.60
ALPHA
Alpha(1) Alpha(2)
DLY 0.55 -0.01
(5.95) (-1.00)
DLC 0.00 0.00
(0.00) (0.00)
DLH 0.22 -0.02
(4.66) (-3.31)
DLKP -0.53 -0.07
(-3.00) (-3.41)
PI
LY LC LH LKP
DLY -0.61 0.51 0.04 0.09
(-4.74) (5.19) (2.87) (3.55)
DLC 0.00 0.00 0.00 0.00
(0.00) (0.00) (0.00) (0.00)
DLH -0.17 0.16 0.00 0.01
(-2.53) (3.19) (0.28) (1.05)
DLKP 1.05 -0.76 -0.13 -0.23
(4.22) (-3.98) (-4.50) (-4.49)
Log-Likelihood = 1775.04
THE MA-REPRESENTATION AND DECOMPOSITION OF THE TREND (Restricted Model)
The Coefficients of the Common Trends:
RE-NORMALIZATION OF ALPHA Orthogonal:
ALPHA Orthogonal (transposed)
LY LC LH LKP
CT(1) 0.00 -1.00 0.00 0.00
CT(2) 0.49 0.00 -0.86 0.15
ALPHA Orthogonal (transposed)
LY LC LH LKP
CT(1) 0.00 1.00 0.00 0.00
(.NA) (.NA) (.NA) (.NA)
CT(2) -0.56 0.00 1.00 -0.17
(-4.23) (.NA) (.NA) (-1.83)
The Loadings to the Common Trends, BETA_ORT(tilde):
CT1 CT2
LY 1.25 -0.74
(4.64) (-1.52)
LC 1.16 -0.61
(4.74) (-1.39)
LH 0.91 0.88
(5.04) (2.73)
LKP 1.39 -1.84
(3.51) (-2.59)
The Long-Run Impact Matrix, C
LY LC LH LKP
LY 0.42 1.25 -0.74 0.12
(1.32) (4.64) (-1.52) (0.91)
LC 0.35 1.16 -0.61 0.10
(1.21) (4.74) (-1.39) (0.84)
LH -0.50 0.91 0.88 -0.15
(-2.37) (5.04) (2.73) (-1.63)
LKP 1.03 1.39 -1.84 0.31
(2.24) (3.51) (-2.59) (1.55)
The Linear Trends in the Levels, C*MJU
LY LC LH LKP
0.01 0.01 0.00 0.01
Residual S.E. and Cross-Correlations
LY LC LH LKP
0.00678818 0.00616074 0.00452668 0.00992199
LY 1.00
LC 1.00 1.00
LH 0.47 0.50 1.00
LKP 0.96 0.95 0.20 1.00
THE MA-REPRESENTATION AND DECOMPOSITION OF THE TREND (Restricted Model)
The Coefficients of the Common Trends:
RE-NORMALIZATION OF ALPHA Orthogonal:
ALPHA Orthogonal (transposed)
LY LC LH LKP
CT(1) 0.0000 -1.0000 0.0000 0.0000
CT(2) 0.4854 0.0000 -0.8621 0.1456
ALPHA Orthogonal (transposed)
LY LC LH LKP
CT(1) 0.0000 1.0000 0.0000 0.0000
(.NA) (.NA) (.NA) (.NA)
CT(2) -0.5631 0.0000 1.0000 -0.1689
(-4.2293) (.NA) (.NA) (-1.8272)
The Loadings to the Common Trends, BETA_ORT(tilde):
CT1 CT2
LY 1.2535 -0.7393
(4.6430) (-1.5213)
LC 1.1627 -0.6149
(4.7450) (-1.3942)
LH 0.9078 0.8842
(5.0420) (2.7286)
LKP 1.3855 -1.8369
(3.5109) (-2.5861)
The Long-Run Impact Matrix, C
LY LC LH LKP
LY 0.4162 1.2535 -0.7393 0.1248
(1.3206) (4.6430) (-1.5213) (0.9113)
LC 0.3462 1.1627 -0.6149 0.1038
(1.2103) (4.7450) (-1.3942) (0.8351)
LH -0.4979 0.9078 0.8842 -0.1493
(-2.3687) (5.0420) (2.7286) (-1.6345)
LKP 1.0343 1.3855 -1.8369 0.3102
(2.2450) (3.5109) (-2.5861) (1.5491)
The Linear Trends in the Levels, C*MJU
LY LC LH LKP
0.0067 0.0061 0.0022 0.0093
Residual S.E. and Cross-Correlations
LY LC LH LKP
0.00678818 0.00616074 0.00452668 0.00992199
LY 1.0000
LC 0.9995 1.0000
LH 0.4721 0.5003 1.0000
LKP 0.9574 0.9475 0.1972 1.0000
PARAMETERS OF THE STRUCTURAL MA-MODEL:
X(t) = C(tilde)*SUM(U(i)) + C*(tilde)(L)*U(t) + Deterministics,
where U(t) = [Trans(1), Trans(2); Perm(1), Perm(2)]
*** Convergence of C*-polynomial in 64 steps.
Structural Long-Run Impact Matrix, C(tilde) (Normalized)
Trans(1) Trans(2) Perm(1) Perm(2)
LY -0.0000 0.0000 1.1404 0.2267
LC -0.0000 0.0000 1.0000 -0.0000
LH -0.0000 -0.0000 0.5279 1.0000
LKP -0.0000 -0.0000 1.6738 0.8221
100*Contemporaneous impact, C*(tilde)(0)
Trans(1) Trans(2) Perm(1) Perm(2)
LY 0.3043 -0.0000 0.4161 -0.0500
LC 0.0151 0.2267 0.3330 0.1640
LH 0.0895 -0.1215 0.1253 0.1806
LKP -0.4721 -0.4963 0.5832 -0.3567
100*Impact After 64 Periods:
Trans(1) Trans(2) Perm(1) Perm(2)
LY 0.0000 0.0003 1.5323 0.1410
LC 0.0001 0.0011 1.3399 0.0002
LH -0.0001 -0.0008 0.7135 0.6216
LKP -0.0003 -0.0033 2.2656 0.5107
RE-NORMALIZATION OF B:
Rotation Matrix, B: [U(t) = B*EPS(t)]
EPS(1) EPS(2) EPS(3) EPS(4)
Trans(1) 207.7675 -143.0569 39.3903 -74.9924
Trans(2) -4.5925 191.3493 -269.9379 -48.0047
Perm(1) 69.7942 118.7383 12.5479 51.1734
Perm(2) -154.5148 117.2421 344.0193 -30.6220
Rotation Matrix, B (Normalized)
EPS(1) EPS(2) EPS(3) EPS(4)
Trans(1) 1.0000 -0.6885 0.1896 -0.3609
Trans(2) 0.0170 -0.7089 1.0000 0.1778
Perm(1) 0.5878 1.0000 0.1057 0.4310
Perm(2) -0.4491 0.3408 1.0000 -0.0890
RE-NORMALIZATION OF INVERSE(B):
Inverse Rotation Matrix, INV(B): [EPS(t) = INV(B)*U(t)]
Trans(1) Trans(2) Perm(1) Perm(2)
EPS(1) 0.0030 0.0000 0.0042 -0.0005
EPS(2) 0.0002 0.0023 0.0033 0.0016
EPS(3) 0.0009 -0.0012 0.0013 0.0018
EPS(4) -0.0047 -0.0050 0.0058 -0.0036
Inverse Rotation Matrix, INV(B) (Normalized)
Trans(1) Trans(2) Perm(1) Perm(2)
EPS(1) 1.0000 0.0000 1.3671 -0.1644
EPS(2) 0.0454 0.6808 1.0000 0.4926
EPS(3) 0.7144 -0.9694 1.0000 1.4412
EPS(4) 0.9512 1.0000 -1.1750 0.7186
RESIDUAL ANALYSIS
Residual S.E. and Cross-Correlations
DLY DLC DLH DLKP
0.00517913 0.00435277 0.00266576 0.00967786
DLY 1.0000
DLC 0.5987 1.0000
DLH 0.5095 0.3892 1.0000
DLKP 0.2330 0.0381 0.1035 1.0000
LOG(|Sigma|) = -43.3628
Information Criteria: SC = -41.6431
H-Q = -42.2052
Trace Correlation = 0.4358
Tests for Autocorrelation
Ljung-Box(20): ChiSqr(296) = 436.2777 [0.0000]
LM(1): ChiSqr(16) = 21.8438 [0.1483]
LM(2): ChiSqr(16) = 17.3656 [0.3623]
Test for Normality: ChiSqr(8) = 4.8495 [0.7735]
Test for ARCH:
LM(1): ChiSqr(100) = 92.8154 [0.6820]
LM(2): ChiSqr(200) = 195.7432 [0.5718]
Univariate Statistics
Mean Std.Dev Skewness Kurtosis Maximum Minimum
DLY 0.0000 0.0052 0.0761 4.5658 0.0173 -0.0176
DLC -0.0000 0.0044 -0.0758 3.3754 0.0111 -0.0140
DLH 0.0000 0.0027 0.1790 2.8403 0.0073 -0.0062
DLKP -0.0000 0.0097 -0.0719 2.5824 0.0200 -0.0241
ARCH(2) Normality R-Squared
DLY 0.1981 [0.9057] 11.3532 [0.0034] 0.6129
DLC 0.3729 [0.8299] 1.8913 [0.3884] 0.2820
DLH 0.0188 [0.9906] 0.5056 [0.7766] 0.8095
DLKP 1.3875 [0.4997] 0.2541 [0.8807] 0.7609
Second period analysis with a trend in cointegration relations (the trend was
insignificant and was therefore omitted in the final analysis)
CATS for RATS version 2 - 12/14/2006 15:53
MODEL SUMMARY
Sample: 1981:02 to 2002:01 (84 observations)
Effective Sample: 1981:04 to 2002:01 (82 observations)
Obs. - No. of variables: 72
System variables: LY LC LH LKP
Constant/Trend: Restricted Trend
Lags in VAR: 2
The unrestricted estimates:
BETA(transposed)
LY LC LH LKP TREND
Beta(1) 202.26 -161.98 -19.91 -32.72 -0.02
Beta(2) 86.63 -81.06 2.71 -26.75 0.14
Beta(3) 47.82 18.24 20.27 -23.09 -0.24
Beta(4) 81.98 -27.01 -71.06 -11.87 -0.12
ALPHA
Alpha(1) Alpha(2) Alpha(3) Alpha(4)
DLY -0.00 0.00 -0.00 0.00
(-5.64) (0.53) (-3.32) (0.67)
DLC 0.00 -0.00 -0.00 0.00
(1.15) (-1.58) (-3.16) (1.68)
DLH -0.00 0.00 0.00 0.00
(-4.33) (1.73) (0.17) (2.15)
DLKP 0.00 0.00 -0.00 -0.00
(2.71) (4.95) (-1.44) (-0.15)
PI
LY LC LH LKP TREND
DLY -0.64 0.42 -0.00 0.13 0.00
(-5.00) (4.30) (-0.01) (4.82) (2.98)
DLC 0.04 -0.07 -0.10 0.03 0.00
(0.35) (-0.88) (-2.75) (1.16) (1.04)
DLH -0.16 0.15 -0.02 0.02 0.00
(-2.26) (2.75) (-0.76) (1.33) (0.14)
DLKP 0.89 -0.86 -0.06 -0.19 0.00
(3.74) (-4.69) (-0.77) (-3.76) (3.35)
Log-Likelihood = 1791.33
RE-NORMALIZATION OF THE EIGENVECTORS:
THE EIGENVECTOR(s)(transposed)
LY LC LH LKP TREND
Beta(1) 202.26 -161.98 -19.91 -32.72 -0.02
Beta(2) 86.63 -81.06 2.71 -26.75 0.14
THE MATRICES BASED ON 2 COINTEGRATING VECTORS:
BETA(transposed)
LY LC LH LKP TREND
Beta(1) 1.00 -0.80 -0.10 -0.16 -0.00
Beta(2) -1.07 1.00 -0.03 0.33 -0.00
ALPHA
Alpha(1) Alpha(2)
DLY -0.61 -0.02
(-5.28) (-0.50)
DLC 0.11 0.06
(1.07) (1.47)
DLH -0.25 -0.04
(-4.21) (-1.68)
DLKP 0.55 -0.40
(2.68) (-4.89)
PI
LY LC LH LKP TREND
DLY -0.58 0.46 0.06 0.09 0.00
(-4.66) (4.50) (5.30) (3.77) (1.21)
DLC 0.04 -0.03 -0.01 0.00 -0.00
(0.41) (-0.30) (-1.26) (0.10) (-1.60)
DLH -0.21 0.16 0.03 0.03 0.00
(-3.21) (3.02) (4.40) (2.20) (2.24)
DLKP 0.98 -0.84 -0.04 -0.22 0.00
(4.39) (-4.59) (-2.00) (-5.17) (4.48)
Log-Likelihood = 1778.96
TEST OF RESTRICTED MODEL: CHISQR(3) = 3.56 [0.31]
RE-NORMALIZATION OF THE EIGENVECTORS:
THE EIGENVECTOR(s)(transposed)
LY LC LH LKP TREND
Beta(1) 62.40 0.00 -24.41 -37.99 0.00
Beta(2) 177.29 -177.29 0.00 -11.56 -0.01
THE MATRICES BASED ON 2 COINTEGRATING VECTORS:
BETA(transposed)
LY LC LH LKP TREND
Beta(1) 1.00 0.00 -0.39 -0.61 0.00
(.NA) (.NA) (-11.14) (-17.34) (.NA)
Beta(2) -1.00 1.00 0.00 0.07 0.00
(.NA) (.NA) (.NA) (6.14) (0.72)
ALPHA
Alpha(1) Alpha(2)
DLY -0.12 0.51
(-3.49) (5.05)
DLC -0.03 -0.01
(-1.02) (-0.11)
DLH -0.01 0.16
(-0.75) (3.09)
DLKP 0.29 -0.73
(4.41) (-3.84)
PI
LY LC LH LKP TREND
DLY -0.63 0.51 0.05 0.11 0.00
(-4.78) (5.05) (3.49) (3.95) (5.05)
DLC -0.02 -0.01 0.01 0.02 -0.00
(-0.19) (-0.11) (1.02) (0.78) (-0.11)
DLH -0.17 0.16 0.01 0.02 0.00
(-2.55) (3.09) (0.75) (1.33) (3.09)
DLKP 1.02 -0.73 -0.11 -0.23 -0.00
(4.10) (-3.84) (-4.41) (-4.39) (-3.84)
Log-Likelihood = 1777.17
