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Here is how I am interpreting results of a Johansen Cointegration Test and Engel-Granger Test for A and B.

The results:(Using matlab)

jcitest(Y)

ans = 

      r0       r1   
t1    false    false


[h,pValue,stat,cValue] = egcitest(Y,'test',{'t1','t2'})
Warning: Sample size of the data
is more than the maximum size 10000
in the table of critical values.
Using critical value -3.3368 at
maximum size for the test. Compare
asymptotic critical value -3.3362. 
> In egcitest>runTest at 1119
In egcitest at 413 
Warning: Sample size of the data
is more than the maximum size 10000
in the table of critical values.
Using critical value -20.5948 at
maximum size for the test. Compare
asymptotic critical value -20.6074. 
> In egcitest>runTest at 1119
In egcitest at 413 

h =

 0     0


pValue =

0.9897    0.9901


stat =

0.0817    0.2153


cValue =

  -3.3368  -20.5948

From all the above I have drawn some conclusions:

1- Cointegration exists

2- With a high pValue, the cointegration relation is significant and "could" be used with a high confidence for forecasting.

Would be great if someone here can validate or tell me I am wrong. Learning this on my own is a bit tricky.

Thanks

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For Engle-Granger, I can see that you are returned a vector of 2 elements for each of the output arguments, hence you run two tests there.

For the sake of clarity and the education of people interested in the post, we can say that:

  1. Since your $hValues$ are both zero, we can say that there is a failure to reject the Null Hypothesis, which in this case is (by definition) that there is no co-integration. Hence the results of the tests are that the pair is not co-integrated.
  2. Typically a low $pValue$ would indicate a good candidate pair. Here is not the case. With certainty then, the Null holds. Low p-Values indicate that the pair is cointegrated. A pValue of < 0.1 would be a good point to investigate further the properties of these time-series.
  3. t-stat values again very low for being significant.

For your Johansen test the same applies, the 'False' returned, means failure to reject the Null Hypothesis.

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  • $\begingroup$ If at all possible can you point out a pair in forex where cointegration test would come positive? I am going to keep testing but right now I need a test case to get a handle on the interpretation of the tests. Again Thanks. :) $\endgroup$ – user3126171 Nov 24 '14 at 17:57
  • $\begingroup$ Sorry for piling on the comments, I ran a test on another pair. The results are similar i.e. hValues are both zero, pValue = 0.1162, 0.0739, Stat= -2.9780, -18.6619, cValue = -3.3368, -20.5948. If I have understood correctly this is a pair worth investigating further because 2nd pValue is <0.1, how to interpret the t-stat? Thanks. Also is it ok if I keep asking a few more questions? Its confusing and greatly appreciate your help. $\endgroup$ – user3126171 Nov 24 '14 at 18:17
  • $\begingroup$ I am not aware of any FX pair exhibiting co integration (that is, I have not looked into it). If you hValues are zero then clearly you are not rejecting the Null and you cannot count on the pValues as they indeed encapsulate error and they cannot be taking into consideration as the Null is not rejected. If you find the above answer useful, upvote it so that other can benefit from it!! $\endgroup$ – SolitonK Nov 25 '14 at 18:45
  • $\begingroup$ Thanks, still working on it. I have an idea in mind for fx pairing, still working on it but decent results from what I have done earlier using very rudimentary studies. $\endgroup$ – user3126171 Nov 25 '14 at 19:00
  • $\begingroup$ My advice is to take slow and surely. Read econometrics, understand the concepts and then you will learn what quantities and qualities to look for when checking for arbitrage. $\endgroup$ – SolitonK Nov 25 '14 at 19:02

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