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I have found Cointegration based on Engle/ Granger and Johansen. However, Granger-causality is rejected for both variables. How is that possible?

According to theory, if x and y are I(1) and cointegrated, x is Granger causal to y and/or y is Granger causal to x. However, Granger-causality has been rejected in my bivariate case, despite their cointegration relationship.

Did I understand it correctly that there has to be at least one granger causality flow in a bivariate cointegrated system?

Thank you for your answer!

Applying an VECM, I get the following results: with only the -0.022460 being significant...

    Vector Error Correction Estimates   
    Date: 10/28/13   Time: 23:58    
    Included observations: 1113 after adjustments   
    Standard errors in ( ) & t-statistics in [ ]    

    Cointegrating Eq:   CointEq1

    CAD(-1)             1.000000

    NATGAS(-1)          0.067366
                       (0.02646)
                       [ 2.54615]

     C                  -0.077093


Error Correction:   D(CAD)  D(NATGAS)

CointEq1        -0.022460   -0.006601
 (0.00514)   (0.01384)
[-4.37213]  [-0.47714]

D(CAD(-1))  -0.054710    0.029241
  (0.02998)  (0.08073)
[-1.82508]  [ 0.36220]

D(CAD(-2))   0.035656    0.101838
 (0.02996)   (0.08070)
[ 1.18998]  [ 1.26200]

D(NATGAS(-1))   -0.004642   -0.077700
 (0.01120)   (0.03016)
[-0.41449]  [-2.57591]

D(NATGAS(-2))    0.004712    0.056858
 (0.01120)   (0.03016)
[ 0.42067]  [ 1.88491]

C    0.000176   -0.000850
 (0.00019)   (0.00051)
[ 0.92332]  [-1.65571]

 R-squared   0.022437    0.011948
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  • $\begingroup$ It sounds eminently possible, but could you please give more details about your situation? $\endgroup$ – Glen_b Oct 28 '13 at 22:02
  • $\begingroup$ Well theory says that there must be at least one Granger causal flow in a cointegrated system. Thats why I expected Granger causality between the cointegrated variables... $\endgroup$ – user21988 Oct 28 '13 at 22:08
  • $\begingroup$ I meant 'can you give more details relating to the inputs to and output from the tests?'. I see no reason to expect hypothesis tests will always produce results consistent with what you expect the population situation to be. $\endgroup$ – Glen_b Oct 28 '13 at 22:12
  • $\begingroup$ Well, I use financial data. For example, CAD-NaturalGas. The p-value of the adf test on the residuals of the EG-regression is for one pair 0.00068411431039002942, implying that there exists a cointegration relationship. However, after testing for granger-causality, p-values lie in the range of 0.4-0.8 on both sides edit:[daily 1200 observations] $\endgroup$ – user21988 Oct 28 '13 at 22:29
  • $\begingroup$ Thanks, that edit to your question might come closer to saving it from closure, though I expect people might want further clarification. $\endgroup$ – Glen_b Oct 28 '13 at 23:18
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If there is cointegration, then there is (100% percent surely) G-causality, but not vice versa.

For stationarity check, one MUST use Narayan-Popp 2010 non-stationarity test that takes the possible existence of structural breaks in the data into account.

You have 1113 observations after adjustments. This implies about 3-year period. During that period, it is highly likely that crises/interventions occured. These are encoded as structural breaks.

For cointegration check, (in the case of possible structural breaks) one MUST use Johansen-Mosconi-Nielsen 2000 critical values rather than Osterwald-Lenum 1992 critical values.

So, I am of the opinion that if you employ true methods, you will most probably end up with either of the following cases:
1. Your variables are not all I(1); hence, cointegration is impossible.
2. Your variables are all I(1); but, they are not cointegrated.

If I had your data in my hand, I would be able to say which one of the cases is valid.

Note also that one-to-one applying of Joyeux 2007 method via R revealed that Eviews miscalculate cointegration check. Hence, use R no matter what...

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