Trend assumption: Linear deterministic trend
Series: Y X1 X2 X3 X4 X5
Lags interval (in first differences): 1 to 1
Unrestricted Cointegration Rank Test (Trace)
Hypothesized Trace 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**
None * 0.992673 217.4843 95.75366 0.0000
At most 1 * 0.953881 119.1611 69.81889 0.0000
At most 2 * 0.746179 57.63060 47.85613 0.0046
At most 3 * 0.609035 30.20808 29.79707 0.0448
At most 4 0.345000 11.42536 15.49471 0.1867
At most 5 0.137696 2.962946 3.841466 0.0852
Trace test indicates 4 cointegrating eqn(s) at the 0.05 level
* denotes rejection of the hypothesis at the 0.05 level
**MacKinnon-Haug-Michelis (1999) p-values
Unrestricted Cointegration Rank Test (Maximum Eigenvalue)
Hypothesized Max-Eigen 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**
None * 0.992673 98.32320 40.07757 0.0000
At most 1 * 0.953881 61.53051 33.87687 0.0000
At most 2 0.746179 27.42252 27.58434 0.0524
At most 3 0.609035 18.78273 21.13162 0.1033
At most 4 0.345000 8.462411 14.26460 0.3336
At most 5 0.137696 2.962946 3.841466 0.0852
Max-eigenvalue test indicates 2 cointegrating eqn(s) at the 0.05 level
* denotes rejection of the hypothesis at the 0.05 level
**MacKinnon-Haug-Michelis (1999) p-values
Unrestricted Cointegrating Coefficients (normalized by b'*S11*b=I):
Y X1 X2 X3 X4 X5
-127.4000 -19.25329 -3.664874 -42.53775 113.9714 -0.476486
47.82547 13.54631 -7.016553 8.369574 64.36535 90.46661
118.3051 26.38691 -19.13924 -6.770968 155.4215 150.1841
43.95206 44.59194 5.515208 -8.854019 15.84510 47.91734
-28.78988 -50.63966 4.663981 50.50068 -59.91371 -35.55625
-84.45903 -24.90656 9.659422 43.13304 -119.9738 -118.1034
Unrestricted Adjustment Coefficients (alpha):
D(Y) 0.003172 0.010608 -0.004004 0.005571 0.003731
D(X1) 0.011447 -0.011763 0.020158 -0.019252 0.010789
D(X2) 0.024376 0.002122 0.003249 -0.019642 -0.010086
D(X3) 0.009585 -0.010867 -0.004761 -0.000805 0.000207
D(X4) 0.000997 0.000845 -0.000338 0.000553 0.000180
D(X5) -0.005018 -0.005271 -0.006570 -0.004450 -0.001695
1 Cointegrating Equation(s): Log likelihood 390.0177
Normalized cointegrating coefficients (standard error in parentheses)
Y X1 X2 X3 X4 X5
1.000000 0.151125 0.028767 0.333891 -0.894595 0.003740
(0.01096) (0.00382) (0.01559) (0.04377) (0.02679)
Adjustment coefficients (standard error in parentheses)
D(Y) -0.404129
(0.57993)
D(X1) -1.458378
(1.50192)
D(X2) -3.105447
(1.20902)
D(X3) -1.221092
(0.46277)
D(X4) -0.126966
(0.10373)
D(X5) 0.639297
(0.41659)
2 Cointegrating Equation(s): Log likelihood 420.7830
Normalized cointegrating coefficients (standard error in parentheses)
Y X1 X2 X3 X4 X5
1.000000 0.000000 0.229487 0.515635 -3.457302 -2.155677
(0.03085) (0.09036) (0.33487) (0.20677)
0.000000 1.000000 -1.328174 -1.202610 16.95757 14.28898
(0.19895) (0.58272) (2.15945) (1.33338)
Adjustment coefficients (standard error in parentheses)
D(Y) 0.103194 0.082623
(0.45834) (0.07929)
D(X1) -2.020944 -0.379741
(1.53628) (0.26577)
D(X2) -3.003947 -0.440560
(1.28871) (0.22294)
D(X3) -1.740798 -0.331741
(0.24921) (0.04311)
D(X4) -0.086562 -0.007743
(0.10571) (0.01829)
D(X5) 0.387215 0.025213
(0.39387) (0.06814)
3 Cointegrating Equation(s): Log likelihood 434.4942
Normalized cointegrating coefficients (standard error in parentheses)
Y X1 X2 X3 X4 X5
1.000000 0.000000 0.000000 -0.220046 -1.069405 -1.580655
(0.18505) (0.34068) (0.32026)
0.000000 1.000000 0.000000 3.055212 3.137401 10.96098
(1.10444) (2.03329) (1.91146)
0.000000 0.000000 1.000000 3.205771 -10.40539 -2.505691
(0.65624) (1.20815) (1.13576)
Adjustment coefficients (standard error in parentheses)
D(Y) -0.370442 -0.023018 -0.009431
(0.57045) (0.11187) (0.06552)
D(X1) 0.363874 0.152172 -0.345230
(1.74440) (0.34209) (0.20037)
D(X2) -2.619581 -0.354831 -0.166407
(1.69923) (0.33324) (0.19518)
D(X3) -2.304060 -0.457372 0.132244
(0.21824) (0.04280) (0.02507)
D(X4) -0.126519 -0.016655 -0.003116
(0.13896) (0.02725) (0.01596)
D(X5) -0.390029 -0.148145 0.181115
(0.39425) (0.07732) (0.04529)
4 Cointegrating Equation(s): Log likelihood 443.8856
Normalized cointegrating coefficients (standard error in parentheses)
Y X1 X2 X3 X4 X5
1.000000 0.000000 0.000000 0.000000 -1.041138 -1.066745
(0.20980) (0.21054)
0.000000 1.000000 0.000000 0.000000 2.744930 3.825642
(0.48484) (0.48655)
0.000000 0.000000 1.000000 0.000000 -10.81720 -9.992656
(0.70899) (0.71149)
0.000000 0.000000 0.000000 1.000000 0.128460 2.335465
(0.51152) (0.51333)
Adjustment coefficients (standard error in parentheses)
D(Y) -0.125603 0.225385 0.021291 -0.068367
(0.50564) (0.15505) (0.05839) (0.12195)
D(X1) -0.482306 -0.706327 -0.451411 -0.551420
(1.46962) (0.45064) (0.16972) (0.35445)
D(X2) -3.482904 -1.230723 -0.274739 -0.867203
(1.39694) (0.42836) (0.16132) (0.33692)
D(X3) -2.339456 -0.493283 0.127802 -0.459294
(0.22044) (0.06760) (0.02546) (0.05317)
D(X4) -0.102197 0.008020 -6.40E-05 -0.037935
(0.13992) (0.04291) (0.01616) (0.03375)
D(X5) -0.585619 -0.346583 0.156572 0.253226
(0.32837) (0.10069) (0.03792) (0.07920)
5 Cointegrating Equation(s): Log likelihood 448.1168
Normalized cointegrating coefficients (standard error in parentheses)
Y X1 X2 X3 X4 X5
1.000000 0.000000 0.000000 0.000000 0.000000 -0.438958
(0.14289)
0.000000 1.000000 0.000000 0.000000 0.000000 2.170500
(0.31728)
0.000000 0.000000 1.000000 0.000000 0.000000 -3.470083
(1.29369)
0.000000 0.000000 0.000000 1.000000 0.000000 2.258006
(0.15882)
0.000000 0.000000 0.000000 0.000000 1.000000 0.602982
(0.11010)
Adjustment coefficients (standard error in parentheses)
D(Y) -0.233020 0.036446 0.038693 0.120054 0.286799
(0.47001) (0.19064) (0.05489) (0.16888) (0.53162)
D(X1) -0.792910 -1.252659 -0.401093 -0.006587 2.729111
(1.36733) (0.55460) (0.15969) (0.49129) (1.54657)
D(X2) -3.192539 -0.719988 -0.321778 -1.376536 3.712707
(1.30360) (0.52875) (0.15225) (0.46840) (1.47448)
D(X3) -2.345426 -0.503784 0.128770 -0.448821 -0.372221
(0.22280) (0.09037) (0.02602) (0.08005) (0.25200)
D(X4) -0.107374 -0.001086 0.000775 -0.028853 0.113461
(0.14126) (0.05730) (0.01650) (0.05076) (0.15978)
D(X5) -0.536823 -0.260753 0.148667 0.167632 -1.901229
(0.31934) (0.12952) (0.03730) (0.11474) (0.36120)