compute [string] %catsdir = 'C:\CATS\'
source(noecho) &%catsdir+'cats.src'
                    COINTEGRATION ANALYSIS

Endogeneous series   :
RM2         Y           DIFP        IM2         IB

Exogeneous series
Stationary           :
D744        D761        D812
Deterministic series :

Unrestricted constant and trend in coint. space
3 centered seasonal dummies

Effective sample     :  74:03 TO 83:01
Lag(s) in VAR-model  :  2
No. of observations  :  35
Obs.- no.of variables:  17


I(1) ANALYSIS

Eigenv.    L-max   Trace   H0: r     p-r
0.8131   58.70  124.66       0       5
0.6636   38.13   65.96       1       4
0.3895   17.27   27.83       2       3
0.2196    8.68   10.55       3       2
0.0522    1.88    1.88       4       1

BETA (transposed)
RM2     Y       DIFP    IM2     IB         TREND
 -22.709  81.044 -32.075 -43.875-120.384  -0.455
  -4.284  -7.475-130.502 444.304-258.168   0.108
 -25.381  41.250  74.986 416.525-287.732  -0.220
  16.639   8.042  13.093 -51.124  52.222  -0.192
  32.556 -14.819  20.568 202.757 370.660  -0.238


The matrices based on 2 cointegration vectors

BETA (transposed)
    RM2       Y         DIFP      IM2       IB             TREND
    -0.280     1.000    -0.396    -0.541    -1.485    -0.006
     0.033     0.057     1.000    -3.405     1.978    -0.001

ALPHA                               T-VALUES FOR ALPHA
DRM2          -0.927  -1.011       -7.802  -5.284
DY            -0.312   0.477       -3.525   3.352
DDIFP          0.406  -0.377        4.081  -2.357
DIM2          -0.009   0.049       -1.482   4.795
DIB            0.048   0.045        2.731   1.582

PI
                 RM2       Y         DIFP      IM2       IB             TREND
DRM2             0.227    -0.985    -0.644     3.944    -0.623     0.006
DY               0.103    -0.284     0.600    -1.456     1.407     0.001
DDIFP           -0.126     0.384    -0.538     1.065    -1.349    -0.002
DIM2             0.004    -0.007     0.053    -0.163     0.112     0.000
DIB             -0.012     0.051     0.026    -0.180     0.017    -0.000

T-VALUES FOR PI
                 6.687    -8.254    -3.269     6.025    -1.492     8.810
                 4.085    -3.202     4.096    -2.989     4.528     2.657
                -4.447     3.847    -3.263     1.944    -3.861    -3.428
                 2.346    -1.036     5.011    -4.626     4.972     0.337
                -2.391     2.865     0.884    -1.842     0.279    -3.022

The eigenvalues of the companion matrix
      real   complex   modulus    argument
    1.0000    0.0000    1.0000    0.0000
    1.0000    0.0000    1.0000    0.0000
    1.0000    0.0000    1.0000    0.0000
    0.6960    0.0000    0.6960    0.0000
   -0.6780   -0.0000    0.6780   -3.1416
    0.4240   -0.2008    0.4691   -0.4424
    0.4240    0.2008    0.4691    0.4424
    0.0448   -0.1600    0.1661   -1.2980
    0.0448    0.1600    0.1661    1.2980
    0.0000    0.0000    0.0000    0.0000


The LR test, CHISQ(1) =  14.27 , p-value = 0.00

BETA (transposed)
    RM2       Y         DIFP      IM2       IB             TREND
    -0.018    -0.018     0.000     1.000    -0.476     0.000
    -0.269     1.000    -0.656    -0.708    -1.514    -0.005

ALPHA                               T-VALUES FOR ALPHA
DRM2           3.339  -0.564        3.158  -3.621
DY            -2.267  -0.459       -3.594  -4.940
DDIFP         -0.396   0.383       -0.538   3.531
DIM2          -0.178  -0.023       -3.468  -3.096
DIB           -0.061   0.037       -0.449   1.845


Recalculation of the eigenvectors

BETA (transposed)
    RM2       Y         DIFP      IM2       IB             TREND
    -0.261     1.000     0.000    -1.847    -0.687    -0.006
    -0.076     0.214    -0.423     1.000    -1.000    -0.001

"STANDARD ERRORS" FOR BETA (transposed)
     0.042     0.000     0.000     0.843     0.827     0.001
     0.013     0.039     0.056     0.000     0.000     0.000

ALPHA                               T-VALUES FOR ALPHA
DRM2          -1.311   1.523       -9.124   3.269
DY             0.019  -1.420        0.181  -4.096
DDIFP          0.112   1.272        0.933   3.263
DIM2           0.020  -0.125        2.615  -5.011
DIB            0.064  -0.061        2.993  -0.884


The LR test, CHISQ(4) =   9.69 , p-value = 0.05

BETA (transposed)
    RM2       Y         DIFP      IM2       IB             TREND
    -0.229     1.000     0.000    -2.059     0.000    -0.006
     0.000     0.000     1.000    -0.432     0.432     0.000

"STANDARD ERRORS" FOR BETA (transposed)
     0.024     0.000     0.000     0.591     0.000     0.000
     0.000     0.000     0.000     0.215     0.215     0.000

ALPHA                               T-VALUES FOR ALPHA
DRM2          -1.020  -0.576       -8.066  -2.532
DY            -0.261   0.445       -2.592   2.454
DDIFP          0.391  -0.754        4.315  -4.626
DIM2          -0.005   0.046       -0.727   3.544
DIB            0.051   0.021        2.814   0.656


The LR test, CHISQ(4) =   3.09 , p-value = 0.54

BETA (transposed)
    RM2       Y         DIFP      IM2       IB             TREND
    -0.234     1.000     0.000    -2.322     0.000    -0.006
     0.000     0.000    -0.504     1.000    -0.496     0.000


ALPHA                               T-VALUES FOR ALPHA
DRM2          -1.015   1.261       -8.413   3.007
DY            -0.263  -1.078       -2.747  -3.243
DDIFP          0.390   1.332        4.140   4.069
DIM2          -0.005  -0.107       -0.802  -4.630
DIB            0.051  -0.051        2.827  -0.811


The LR test, CHISQ(3) =   9.85 , p-value = 0.02

BETA (transposed)
    RM2       Y         DIFP      IM2       IB             TREND
     0.000     0.000     1.000    -0.212     0.000     0.000
    -0.275     1.000    -0.203    -0.959    -1.228    -0.006

ALPHA                               T-VALUES FOR ALPHA
DRM2          -0.653  -1.033       -2.562  -7.415
DY             0.442  -0.259        2.472  -2.653
DDIFP         -0.695   0.338       -4.127   3.668
DIM2           0.041  -0.004        2.954  -0.548
DIB            0.054   0.055        1.652   3.104


The LR test, CHISQ(3) =   9.80 , p-value = 0.02

BETA (transposed)
    RM2       Y         DIFP      IM2       IB             TREND
     0.000     0.000     1.000     0.000     0.107     0.000
    -0.277     1.000     0.000    -0.826    -1.275    -0.006

"STANDARD ERRORS" FOR BETA (transposed)
     0.000     0.000     0.000     0.000     0.141     0.000
     0.041     0.000     0.000     0.838     0.826     0.001

ALPHA                               T-VALUES FOR ALPHA
DRM2          -0.489  -1.006       -1.936  -7.320
DY             0.458  -0.279        2.534  -2.836
DDIFP         -0.789   0.360       -4.757   3.984
DIM2           0.043  -0.006        3.138  -0.774
DIB            0.030   0.053        0.907   2.928


The LR test, CHISQ(3) =  21.64 , p-value = 0.00

BETA (transposed)
    RM2       Y         DIFP      IM2       IB             TREND
     0.000     0.000     0.000     1.000    -0.512     0.000
    -0.285     1.000    -0.454    -3.480     0.000    -0.006

"STANDARD ERRORS" FOR BETA (transposed)
     0.000     0.000     0.000     0.000     0.048     0.000
     0.025     0.000     0.152     0.593     0.000     0.000

ALPHA                               T-VALUES FOR ALPHA
DRM2           0.570  -0.850        0.447  -5.736
DY            -2.075  -0.340       -2.438  -3.440
DDIFP          0.727   0.404        0.794   3.802
DIM2          -0.211  -0.013       -3.331  -1.815
DIB            0.198   0.048        1.241   2.591



The LR test, CHISQ(3) =   1.94 , p-value = 0.58

BETA (transposed)
    RM2       Y         DIFP      IM2       IB             TREND
     0.000     0.000    -0.507     1.000    -0.493     0.000
    -0.277     1.000    -0.718     0.000    -1.721    -0.006


ALPHA                               T-VALUES FOR ALPHA
DRM2           2.698  -0.996        6.036  -8.016
DY            -0.678  -0.281       -2.014  -3.007
DDIFP          0.783   0.375        2.282   3.931
DIM2          -0.098  -0.006       -4.125  -0.919
DIB           -0.125   0.052       -1.947   2.879

No converg!
The LR test, CHISQ(3) =  10.29 , p-value = 0.02

BETA (transposed)
    RM2       Y         DIFP      IM2       IB             TREND
     0.000     0.000     1.000     0.019    -0.019     0.000
    -0.276     1.000   -68.182    -2.159     0.000    -0.006

"STANDARD ERRORS" FOR BETA (transposed)
     0.000     0.000     0.000     0.012     0.012     0.000
     0.041     0.000     0.154     0.619     0.000     0.001

ALPHA                               T-VALUES FOR ALPHA
DRM2         -70.179  -1.023       -7.383  -7.333
DY           -17.791  -0.268       -2.654  -2.722
DDIFP         22.782   0.346        3.673   3.797
DIM2          -0.288  -0.005       -0.558  -0.638
DIB            3.728   0.054        3.063   3.031

No testing:

BETA (transposed)
    RM2       Y         DIFP      IM2       IB             TREND
    -0.356     1.000    -1.978     4.677    -4.677    -0.005
    -0.025     0.036    -0.323     1.000    -0.677    -0.000


ALPHA                               T-VALUES FOR ALPHA
DRM2          -1.354  10.275       -8.947   9.124
DY            -0.279  -0.152       -2.477  -0.181
DDIFP          0.416  -0.879        3.284  -0.933
DIM2          -0.001  -0.158       -0.119  -2.615
DIB            0.069  -0.503        3.059  -2.993


BETA (transposed)
    RM2       Y         DIFP      IM2       IB             TREND
    -0.245     1.000     0.340    -2.970     0.000    -0.006
    -0.025     0.036    -0.323     1.000    -0.677    -0.000

ALPHA                               T-VALUES FOR ALPHA
DRM2          -1.018   0.921       -8.947   1.492
DY            -0.210  -2.078       -2.477  -4.528
DDIFP          0.313   1.993        3.284   3.861
DIM2          -0.001  -0.165       -0.119  -4.972
DIB            0.052  -0.026        3.059  -0.279


You must normalize to get "Sd. err." for beta
EIGENVECTOR(S) (transposed)
RM2       Y         DIFP      IM2       IB             TREND
  18.6451 -79.9274   0.0000 200.8545   0.0000   0.4933
  11.1014 -15.3748 132.9085-429.2467 296.3382   0.0155

The LR test, CHISQ(1) =   0.46 , p-value = 0.50

BETA (transposed)
    RM2       Y         DIFP      IM2       IB             TREND
    -0.233     1.000     0.000    -2.513     0.000    -0.006
    -0.026     0.036    -0.310     1.000    -0.690    -0.000


ALPHA                               T-VALUES FOR ALPHA
DRM2          -1.053   1.928       -9.083   3.096
DY            -0.207  -1.966       -2.369  -4.189
DDIFP          0.336   1.729        3.459   3.313
DIM2          -0.001  -0.170       -0.092  -5.033
DIB            0.053  -0.074        2.995  -0.787



THE MA-REPRESENTATION AND DECOMPOSITION OF THE TREND

The orthogonal complement to alpha
(The coefficients to the common trends (transposed))
  RM2       Y         DIFP      IM2       IB
     0.054     0.000     0.014     0.321     1.000
     0.124     1.000     1.027     0.353    -0.135
    -0.021    -0.233    -0.157     1.000    -0.317

The loadings to the common trends
    -2.476     0.783    19.813
     1.474     0.705     6.141
     1.229     0.984     3.976
     0.816     0.208     0.604
     0.801    -0.133    -1.331

The impact-matrix for the MA-representation: C(1)
  RM2       Y         DIFP      IM2       IB
    -0.448    -3.827    -2.336    19.295    -8.868
     0.040    -0.723    -0.217     6.863    -0.570
     0.107     0.059     0.405     4.718    -0.166
     0.058     0.067     0.130     0.940     0.597
     0.055     0.177     0.084    -1.121     1.241

"t-values" for C(1)
    -0.721    -1.683    -1.558     0.988    -1.785
     0.418    -2.040    -0.930     2.254    -0.735
     1.735     0.263     2.727     2.441    -0.337
     2.033     0.650     1.904     1.054     2.630
     1.346     1.194     0.854    -0.880     3.830

The long-run covariance matrix: C(1)*Sigma*C(1)'
  RM2       Y         DIFP      IM2       IB
    0.0015
    0.0002    0.0000
   -0.0001   -0.0000    0.0000
   -0.0001   -0.0000    0.0000    0.0000
   -0.0001   -0.0000    0.0000    0.0000    0.0000

The linear trends in the levels
  RM2       Y         DIFP      IM2       IB
    0.0069    0.0076   -0.0002   -0.0001    0.0001


  The short-run matrices

The lagged endogenous variables

Time: t-1

      DRM2        DY     DDIFP      DIM2       DIB
    -1.082     0.051     0.000    -6.712    -3.233
     0.316     0.298    -0.000    -0.718     0.258
     0.462    -0.017     0.000     3.710     2.363
     0.010     0.019     0.000     0.378     0.117
     0.044     0.015    -0.000     0.077     0.096

t-values
   -10.277     0.448     2.149    -3.983    -3.496
     3.977     3.505    -0.952    -0.565     0.370
     5.231    -0.184     0.925     2.628     3.049
     1.762     3.088     0.068     4.136     2.328
     2.779     0.859    -1.183     0.302     0.684

The exogenous I(0) variables

D744     D761     D812
   -0.064    0.023   -0.022
   -0.039   -0.006    0.003
   -0.001    0.009   -0.004
   -0.000    0.001    0.000
    0.002    0.006    0.007

t-values
   -5.800    2.441   -2.289
   -4.627   -0.795    0.431
   -0.110    1.116   -0.509
   -0.766    1.999    0.366
    0.926    4.281    4.856

The deterministic variables

 SEA(1) SEA(2) SEA(3)  CONST
  0.043  0.096  0.118 10.684
 -0.059  0.044 -0.124  2.672
 -0.024  0.003 -0.061 -3.982
 -0.002 -0.000 -0.004  0.047
 -0.003 -0.001 -0.010 -0.539

t-values
  5.106 16.657  7.423  8.656
 -9.140 10.216-10.358  2.873
 -3.329  0.691 -4.572 -3.849
 -3.676 -0.751 -4.085  0.708
 -2.711 -1.425 -4.093 -2.882

                     COINTEGRATION ANALYSIS

Endogeneous series   :
RM2         Y           DIFP        IM2         IB

Exogeneous series
Stationary           :
D744        D761        D812
Deterministic series :

Unrestricted constant and trend in coint. space
3 centered seasonal dummies

Effective sample     :  74:03 TO 83:01
Lag(s) in VAR-model  :  2
No. of observations  :  35
Obs.- no.of variables:  17


Batch tests of the time series properties of the individual series

TEST FOR EXCLUSION: LR TEST CHISQ(r)
   r DGF CHISQ_5RM2     Y       DIFP    IM2     IB         TREND
   1   1    3.84   16.14   20.38    1.40    0.16    1.87   16.88
   2   2    5.99   17.28   33.25   18.16    9.81    6.92   19.57
   3   3    7.81   22.25   41.10   26.65   16.56    9.81   20.89
   4   4    9.49   24.49   42.11   33.11   16.73    9.86   21.37

TEST FOR STATIONARITY: LR TEST CHISQ(p-r)
   r DGF CHISQ_5   RM2     Y       DIFP    IM2     IB
   1   5   11.07   43.29   35.36   30.15   51.20   48.06
   2   4    9.49   28.96   25.74   10.13   32.92   29.91
   3   3    7.81   10.14   10.92    2.35   12.07    9.99
   4   2    5.99    3.48    4.63    1.84    3.61    1.76

TEST FOR WEAK-EXOGENEITY: LR TEST CHISQ(r)
   r DGF CHISQ_5    RM2     Y       DIFP    IM2     IB
   1   1    3.84   11.44    5.67    8.55    0.85    5.49
   2   2    5.99   31.13   14.79   13.57   16.54    8.20
   3   3    7.81   38.70   17.20   21.66   18.27    8.42
   4   4    9.49   43.84   23.91   26.63   19.50   11.85

