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### Informations about Signal Coefficients on a VEC Output

Posted: Tue Dec 04, 2018 7:11 am
Dear,

I want help with the output coefficient signals of my VEC model.

In the first part of the cointegration equation, we have some coefficientes with signals, but when I put them on a paper for analysis and discussion, the signals will be exchanged, correct?

VEC Estimation Output from Eviews:

Vector Error Correction Estimates
Date: 12/04/18 Time: 11:56
Sample (adjusted): 2001M09 2009M12
Included observations: 100 after adjustments
Standard errors in ( ) & t-statistics in [ ]

Cointegrating Eq: CointEq1

LPE(-1) 1.000000

LPG(-1) -1.217436
(0.19909)
[-6.11487]

LPS(-1) -0.206260
(0.04987)
[-4.13582]

C 1.193296

Error Correction: D(LPE) D(LPG) D(LPS)

CointEq1 -0.402196 -0.018656 -0.187457
(0.07665) (0.03805) (0.14247)
[-5.24747] [-0.49027] [-1.31576]

D(LPE(-1)) 0.442810 0.022982 -0.169454
(0.09965) (0.04948) (0.18524)
[ 4.44349] [ 0.46450] [-0.91479]

D(LPG(-1)) -0.267557 0.219323 0.697048
(0.23841) (0.11837) (0.44316)
[-1.12227] [ 1.85292] [ 1.57292]

D(LPS(-1)) 0.033195 0.029062 0.168786
(0.05993) (0.02976) (0.11141)
[ 0.55385] [ 0.97664] [ 1.51503]

C -0.000375 -0.001082 0.003117
(0.00454) (0.00225) (0.00843)
[-0.08266] [-0.48050] [ 0.36963]

R-squared 0.374921 0.090392 0.106385
Adj. R-squared 0.348602 0.052092 0.068759
Sum sq. resids 0.194794 0.048017 0.673053
S.E. equation 0.045282 0.022482 0.084171
F-statistic 14.24518 2.360139 2.827429
Log likelihood 170.1554 240.1751 108.1612
Akaike AIC -3.303108 -4.703503 -2.063224
Schwarz SC -3.172850 -4.573244 -1.932966
Mean dependent -0.000161 -0.001329 0.002472
S.D. dependent 0.056105 0.023091 0.087223

Determinant resid covariance (dof adj.) 5.23E-09
Determinant resid covariance 4.49E-09
Log likelihood 535.4082
Akaike information criterion -10.34816
Schwarz criterion -9.879234

Let me explain: the negative signal of the LPG coefficient is actually positive, correct? The negative signal of the LPS coefficient is actually positive and the positive signal of the constant will actually be negative, correct?

The true signals are the opposite, correct?

Example: VEC Output

LPG(-1) -1.217436 , the true value is 1.217436?
LPS(-1) -0.206260, the true value is 0.206260?
c 1.193296, the true value is -1.193296?

Best Regards, José.

### Re: Informations about Signal Coefficients on a VEC Output

Posted: Tue Dec 04, 2018 8:19 am
If your underlying question is what is the actual co-integrating relationship, then yes, the signs are in fact reversed. Thus, in your case, the co-integrating relationship is

Code: Select all

`LPE(-1) = 1.217436*LPG(-1) + 0.206260*LPS(-1) - 1.193296`

### Re: Informations about Signal Coefficients on a VEC Output

Posted: Tue Dec 04, 2018 8:25 am
Thanks a lot, Mirza.

And the signals from the Error Correction equation stay the same as we see at the Eviews, correct?

Error Correction: D(LPE) D(LPG) D(LPS)

CointEq1 -0.402196 -0.018656 -0.187457
(0.07665) (0.03805) (0.14247)
[-5.24747] [-0.49027] [-1.31576]

D(LPE(-1)) 0.442810 0.022982 -0.169454
(0.09965) (0.04948) (0.18524)
[ 4.44349] [ 0.46450] [-0.91479]

D(LPG(-1)) -0.267557 0.219323 0.697048
(0.23841) (0.11837) (0.44316)
[-1.12227] [ 1.85292] [ 1.57292]

D(LPS(-1)) 0.033195 0.029062 0.168786
(0.05993) (0.02976) (0.11141)
[ 0.55385] [ 0.97664] [ 1.51503]

C -0.000375 -0.001082 0.003117
(0.00454) (0.00225) (0.00843)
[-0.08266] [-0.48050] [ 0.36963]

Best Regards, José.

### Re: Informations about Signal Coefficients on a VEC Output

Posted: Tue Dec 04, 2018 8:35 am
Indeed. In fact, if you go to View and then Representations, and search among that output, you'll see that the VEC equation for your co-integrating relationship is in fact:

Code: Select all

`D(LPE)=-0.402196*(LPE(-1)-1.217436*LPG(-1)-0.206260*LPS(-1)+1.193296)+0.442810*D(LPE(-1))-0.267557*D(LPG(-1)) ... etc`

### Re: Informations about Signal Coefficients on a VEC Output

Posted: Tue Dec 04, 2018 12:11 pm
Thanks a lot, Mizra.

Now a new doubt has arisen, Would the value of the long-term coefficient of lpg (-1) be the multiplication of the coefficient of cointegration -0.402196 by the coefficient of lpg (-1) within the parentheses (-1.217436)?

Best Regards, José.

### Re: Informations about Signal Coefficients on a VEC Output

Posted: Tue Dec 04, 2018 12:15 pm
If I understand your question correctly, you are wondering about the alpha*beta' partialization of the cointegrating matrix? If this indeed the case, then the answer is no since alpha*beta' = -0.402196 for this co-integrating relationship. In other words,-1.217436 is an element of beta, which is the cointegrating vector (matrix).

### Re: Informations about Signal Coefficients on a VEC Output

Posted: Wed Dec 05, 2018 5:50 pm
Thanks a lot, Mizra!