请问大佬们,Johansen协整检验的结果怎么看啊,我有4个解释变量,1个被解释变量,还有协整通过后必须做误差修正吗?
可以直接做多元线性回归吗?做完多元线性回归还需要做其他的检验吗?小白真的啥也不懂,请求大佬们解答小白的疑惑吧

Date: 04/16/19 Time: 21:44
Sample (adjusted): 1994 2017
Included observations: 24 after adjustments
Trend assumption: Linear deterministic trend (restricted)
Series: Y X1 X2 X3 X4
Lags interval (in first differences): 1 to 2
Unrestricted Cointegration Rank Test (Trace)
Hypothesized Trace 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**
None * 0.959484 208.4095 88.80380 0.0000
At most 1 * 0.931407 131.4640 63.87610 0.0000
At most 2 * 0.754451 67.15448 42.91525 0.0000
At most 3 * 0.575779 33.45224 25.87211 0.0047
At most 4 * 0.415117 12.87224 12.51798 0.0436
Trace test indicates 5 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 * 0.959484 76.94548 38.33101 0.0000
At most 1 * 0.931407 64.30953 32.11832 0.0000
At most 2 * 0.754451 33.70224 25.82321 0.0037
At most 3 * 0.575779 20.58000 19.38704 0.0334
At most 4 * 0.415117 12.87224 12.51798 0.0436
Max-eigenvalue test indicates 5 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 @TREND(92)
-0.000440 0.022385 -0.008633 -0.000108 -0.151775 0.451965
0.002945 -0.038490 -0.014361 0.001376 0.073365 -0.913690
0.001564 -0.017726 -0.004636 0.000427 -0.093215 0.307930
-0.003075 0.015831 -0.019140 0.000640 0.037406 0.722048
0.002108 -0.022066 -0.004394 0.000241 0.128090 -0.358617
Unrestricted Adjustment Coefficients (alpha):
D(Y) 62.60569 108.7943 94.69019 154.6934 -3.915341
D(X1) -45.52801 5.612044 55.25576 3.433003 -8.760363
D(X2) -40.81653 1.054003 39.28766 24.70504 -16.12479
D(X3) -440.8556 -1282.132 1606.169 580.0986 -176.9492
D(X4) 1.932650 2.007154 0.111858 -1.014138 -3.244704
1 Cointegrating Equation(s): Log likelihood -669.4080
Normalized cointegrating coefficients (standard error in parentheses)
Y X1 X2 X3 X4 @TREND(92)
1.000000 -50.86803 19.61779 0.246506 344.8939 -1027.046
(3.93502) (4.08387) (0.19716) (34.9301) (111.090)
Adjustment coefficients (standard error in parentheses)
D(Y) -0.027550
(0.03272)
D(X1) 0.020035
(0.00840)
D(X2) 0.017962
(0.00783)
D(X3) 0.194004
(0.30732)
D(X4) -0.000850
(0.00071)
2 Cointegrating Equation(s): Log likelihood -637.2533
Normalized cointegrating coefficients (standard error in parentheses)
Y X1 X2 X3 X4 @TREND(92)
1.000000 0.000000 -13.34375 0.543368 -85.71804 -62.39258
(1.77768) (0.07122) (9.75577) (47.9265)
0.000000 1.000000 -0.647982 0.005836 -8.465277 18.96384
(0.10996) (0.00441) (0.60347) (2.96460)
Adjustment coefficients (standard error in parentheses)
D(Y) 0.292883 -2.786090
(0.20073) (3.00126)
D(X1) 0.036564 -1.235160
(0.05665) (0.84699)
D(X2) 0.021066 -0.954253
(0.05301) (0.79263)
D(X3) -3.582278 39.48106
(1.76361) (26.3690)
D(X4) 0.005061 -0.033993
(0.00452) (0.06755)
3 Cointegrating Equation(s): Log likelihood -620.4022
Normalized cointegrating coefficients (standard error in parentheses)
Y X1 X2 X3 X4 @TREND(92)
1.000000 0.000000 0.000000 -0.352942 -392.6247 2022.020
(0.15494) (74.2225) (384.236)
0.000000 1.000000 0.000000 -0.037689 -23.36887 120.1843
(0.00762) (3.65186) (18.9050)
0.000000 0.000000 1.000000 -0.067171 -23.00002 156.2089
(0.01181) (5.65962) (29.2988)
Adjustment coefficients (standard error in parentheses)
D(Y) 0.440987 -4.464615 -2.541841
(0.20725) (2.95280) (1.07116)
D(X1) 0.122989 -2.214651 0.056269
(0.03486) (0.49669) (0.18018)
D(X2) 0.082516 -1.650685 0.155084
(0.04615) (0.65758) (0.23854)
D(X3) -1.070090 11.00933 14.77127
(1.23927) (17.6565) (6.40507)
D(X4) 0.005236 -0.035976 -0.046027
(0.00510) (0.07269) (0.02637)
4 Cointegrating Equation(s): Log likelihood -610.1122
Normalized cointegrating coefficients (standard error in parentheses)
Y X1 X2 X3 X4 @TREND(92)
1.000000 0.000000 0.000000 0.000000 -6.573380 -476.6329
(15.8737) (91.3701)
0.000000 1.000000 0.000000 0.000000 17.85628 -146.6386
(5.12640) (29.5078)
0.000000 0.000000 1.000000 0.000000 50.47202 -319.3268
(9.83577) (56.6152)
0.000000 0.000000 0.000000 1.000000 1093.811 -7079.509
(219.682) (1264.50)
Adjustment coefficients (standard error in parentheses)
D(Y) -0.034719 -2.015679 -5.502707 0.282441
(0.19347) (2.14252) (1.09763) (0.06708)
D(X1) 0.112432 -2.160303 -0.009439 0.038480
(0.04702) (0.52069) (0.26675) (0.01630)
D(X2) 0.006544 -1.259582 -0.317776 0.038496
(0.05342) (0.59163) (0.30310) (0.01852)
D(X3) -2.853983 20.19281 3.668055 -0.657915
(1.49561) (16.5629) (8.48531) (0.51860)
D(X4) 0.008355 -0.052031 -0.026616 0.001950
(0.00678) (0.07511) (0.03848) (0.00235)