协整关系表达式如何得到？

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Johensen协整检验结果如下：

Date: 07/21/08   Time: 17:01    
Sample (adjusted): 1988 2006    
Included observations: 19 after adjustments    
Trend assumption: Linear deterministic trend    
Series: VG VS VO VD     
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 *  0.988915  112.2186  47.85613  0.0000
At most 1  0.521762  26.67703  29.79707  0.1098
At most 2  0.377865  12.66176  15.49471  0.1278
At most 3  0.174537  3.644400  3.841466  0.0563
    
 Trace test indicates 1 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 *  0.988915  85.54161  27.58434  0.0000
At most 1  0.521762  14.01527  21.13162  0.3638
At most 2  0.377865  9.017361  14.26460  0.2847
At most 3  0.174537  3.644400  3.841466  0.0563
    
 Max-eigenvalue test indicates 1 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):     
    
VG VS VO VD 
-16.73022 -4.224645 -8.768425  4.106523 
-0.996476  8.641573  11.12774 -0.383862 
-3.827471  10.59676 -4.955695 -6.063728 
-5.548082  0.229217  5.964940 -3.568511 
    
    
 Unrestricted Adjustment Coefficients (alpha):     
    
D(VG)  0.178806  0.004352  0.024482  0.012064
D(VS) -0.014110 -0.031977  0.009283  0.011052
D(VO) -0.011146 -0.000972  0.035721 -0.015025
D(VD) -0.011678  0.059559  0.033221  0.016874
    
    
1 Cointegrating Equation(s):   Log likelihood  116.4943 
    
Normalized cointegrating coefficients (standard error in parentheses)    
VG VS VO VD 
 1.000000  0.252516  0.524107 -0.245455 
  (0.03010)  (0.03097)  (0.01695) 
    
Adjustment coefficients (standard error in parentheses)    
D(VG) -2.991462   
  (0.29586)   
D(VS)  0.236056   
  (0.29979)   
D(VO)  0.186474   
  (0.38124)   
D(VD)  0.195383   
  (0.59419)   
    
    
2 Cointegrating Equation(s):   Log likelihood  123.5019 
    
Normalized cointegrating coefficients (standard error in parentheses)    
VG VS VO VD 
 1.000000  0.000000  0.193314 -0.227611 
   (0.12750)  (0.05068) 
 0.000000  1.000000  1.309990 -0.070667 
   (0.49249)  (0.19575) 
    
Adjustment coefficients (standard error in parentheses)    
D(VG) -2.995799 -0.717784  
  (0.29539)  (0.16953)  
D(VS)  0.267921 -0.216725  
  (0.24141)  (0.13855)  
D(VO)  0.187442  0.038690  
  (0.38188)  (0.21917)  
D(VD)  0.136034  0.564022  
  (0.49356)  (0.28327)  
    
    
3 Cointegrating Equation(s):   Log likelihood  128.0106 
    
Normalized cointegrating coefficients (standard error in parentheses)    
VG VS VO VD 
 1.000000  0.000000  0.000000 -0.293689 
    (0.07802) 
 0.000000  1.000000  0.000000 -0.518447 
    (0.17074) 
 0.000000  0.000000  1.000000  0.341820 
    (0.17841) 
    
Adjustment coefficients (standard error in parentheses)    
D(VG) -3.089502 -0.458357 -1.640742 
  (0.26856)  (0.22357)  (0.23447) 
D(VS)  0.232390 -0.118354 -0.278119 
  (0.24185)  (0.20133)  (0.21115) 
D(VO)  0.050722  0.417215 -0.090102 
  (0.33397)  (0.27802)  (0.29158) 
D(VD)  0.008880  0.916061  0.600526 
  (0.46911)  (0.39052)  (0.40956) 
    
    

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关键词：协整关系 表达式 coefficients unrestricted observations 关系 表达

类似下面的：

根据估计的β和γ得到变量间的协整关系表达式为:
G=-7.348340FD+0.211134FE+7.566352CI+3.644167
　(18.1974)　　(-12.3088)　(-20.1970)　　(2)