johansen检验的结果是这样的,为什么迹检验法的检验结果显示:1、在5%的临界水平下,最多存在2个协整关系的时候(红色字体),p值是大于0.05的,是接受原假设的;到了最多存在3个协整关系的时候(蓝色字体),p值是小于0.05的,又拒绝原假设呢?
2、为什么迹检验的结果(绿色字体)写的是存在两个协整关系,下面有三个方程(绿色字体)呢?
Date: 02/05/15 Time: 13:03
Sample (adjusted): 2001 2013
Included observations: 13 after adjustments
Trend assumption: Linear deterministic trend
Series: LNY LNR LNN LNL
Lags interval (in first differences): No lags
Unrestricted Cointegration Rank Test (Trace)
Hypothesized Trace 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**
None * 0.913220 71.38224 47.85613 0.0001
At most 1 * 0.860580 39.60529 29.79707 0.0027
At most 2 0.483922 13.99187 15.49471 0.0832
At most 3 * 0.339527 5.392395 3.841466 0.0202
Trace 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 Cointegration Rank Test (Maximum Eigenvalue)
Hypothesized Max-Eigen 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**
None * 0.913220 31.77696 27.58434 0.0136
At most 1 * 0.860580 25.61342 21.13162 0.0109
At most 2 0.483922 8.599474 14.26460 0.3210
At most 3 * 0.339527 5.392395 3.841466 0.0202
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):
LNY LNR LNN LNL
-20.16481 2.541668 5.873753 22.73954
0.649353 -0.406979 -8.812658 16.95556
5.881095 -2.151952 5.931433 -19.21651
7.828858 1.024882 -7.583222 -11.66450
Unrestricted Adjustment Coefficients (alpha):
D(LNY) 0.027508 0.008737 0.015021 0.008883
D(LNR) -0.089401 0.437679 0.028577 -0.004035
D(LNN) 0.000861 0.033558 0.003073 0.049176
D(LNL) 0.000818 -0.018861 0.026779 0.006486
1 Cointegrating Equation(s): Log likelihood 70.75439
Normalized cointegrating coefficients (standard error in parentheses)
LNY LNR LNN LNL
1.000000 -0.126045 -0.291287 -1.127685
(0.01133) (0.05847) (0.09939)
Adjustment coefficients (standard error in parentheses)
D(LNY) -0.554684
(0.17823)
D(LNR) 1.802751
(2.88455)
D(LNN) -0.017352
(0.55891)
D(LNL) -0.016504
(0.27320)
2 Cointegrating Equation(s): Log likelihood 83.56109
Normalized cointegrating coefficients (standard error in parentheses)
LNY LNR LNN LNL
1.000000 0.000000 3.051812 -7.984770
(0.48226) (1.01179)
0.000000 1.000000 26.52312 -54.40200
(3.79883) (7.96993)
Adjustment coefficients (standard error in parentheses)
D(LNY) -0.549011 0.066359
(0.17021) (0.02172)
D(LNR) 2.086960 -0.405354
(1.11388) (0.14211)
D(LNN) 0.004439 -0.011470
(0.52061) (0.06642)
D(LNL) -0.028752 0.009756
(0.24810) (0.03165)
3 Cointegrating Equation(s): Log likelihood 87.86083
Normalized cointegrating coefficients (standard error in parentheses)
LNY LNR LNN LNL
1.000000 0.000000 0.000000 -1.934788
(0.12700)
0.000000 1.000000 0.000000 -1.821961
(0.99337)
0.000000 0.000000 1.000000 -1.982423
(0.06928)
Adjustment coefficients (standard error in parentheses)
D(LNY) -0.460670 0.034034 0.173671
(0.14959) (0.02388) (0.08640)
D(LNR) 2.255022 -0.466849 -4.212737
(1.14602) (0.18296) (0.66196)
D(LNN) 0.022510 -0.018083 -0.272455
(0.54192) (0.08652) (0.31302)
D(LNL) 0.128736 -0.047870 0.329862
(0.19492) (0.03112) (0.11259)