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雷达卡
Johansen检验的结果已经出来了，我能通过第一个表判断出存在两个协整关系，可是为什么后面的结果出现了三个标准化的协整方程啊？这个结果分析完了之后我应该做什么呢？
Date: 02/03/15 Time: 08:52
Sample (adjusted): 2001 2013
Included observations: 13 after adjustments
Trend assumption: Linear deterministic trend
Series: LNY LNL LNR LNN
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 LNL LNR LNN
20.16481 -22.73954 -2.541668 -5.873753
-0.649353 -16.95556 0.406979 8.812658
-5.881095 19.21651 2.151952 -5.931433
7.828858 -11.66450 1.024882 -7.583222
Unrestricted Adjustment Coefficients (alpha):
D(LNY) -0.027508 -0.008737 -0.015021 0.008883
D(LNL) -0.000818 0.018861 -0.026779 0.006486
D(LNR) 0.089401 -0.437679 -0.028577 -0.004035
D(LNN) -0.000861 -0.033558 -0.003073 0.049176
1 Cointegrating Equation(s): Log likelihood 70.75439
Normalized cointegrating coefficients (standard error in parentheses)
LNY LNL LNR LNN
1.000000 -1.127685 -0.126045 -0.291287
(0.09939) (0.01133) (0.05847)
Adjustment coefficients (standard error in parentheses)
D(LNY) -0.554684
(0.17823)
D(LNL) -0.016504
(0.27320)
D(LNR) 1.802751
(2.88455)
D(LNN) -0.017352
(0.55891)
2 Cointegrating Equation(s): Log likelihood 83.56109
Normalized cointegrating coefficients (standard error in parentheses)
LNY LNL LNR LNN
1.000000 0.000000 -0.146773 -0.841078
(0.02167) (0.05849)
0.000000 1.000000 -0.018382 -0.487539
(0.01669) (0.04506)
Adjustment coefficients (standard error in parentheses)
D(LNY) -0.549011 0.773655
(0.17021) (0.23931)
D(LNL) -0.028752 -0.301193
(0.24810) (0.34881)
D(LNR) 2.086960 5.388162
(1.11388) (1.56604)
D(LNN) 0.004439 0.588563
(0.52061) (0.73194)
3 Cointegrating Equation(s): Log likelihood 87.86083
Normalized cointegrating coefficients (standard error in parentheses)
LNY LNL LNR LNN
1.000000 0.000000 0.000000 -0.975971
(0.06981)
0.000000 1.000000 0.000000 -0.504433
(0.01666)
0.000000 0.000000 1.000000 -0.919058
(0.48051)
Adjustment coefficients (standard error in parentheses)
D(LNY) -0.460670 0.485000 0.034034
(0.14959) (0.24387) (0.02388)
D(LNL) 0.128736 -0.815786 -0.047870
(0.19492) (0.31778) (0.03112)
D(LNR) 2.255022 4.839019 -0.466849
(1.14602) (1.86840) (0.18296)
D(LNN) 0.022510 0.529515 -0.018083
(0.54192) (0.88352) (0.08652)
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