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I am not able to interpret the following result output for gretl for co-integration:

Rank $\ $ Eigenvalue $\ \ $ Trace test $\ \ $ p-value $\ \ $ Lmax test $\ $ p-value
0 $\ \ \ \ \ \ \ $ 0.032753 $\ \ \ \ \ \ $ 147.61 $\ \ \ \ $ [0.0000] $\ \ \ $ 63.405 $\ \ \ $ [0.0000]
1 $\ \ \ \ \ \ \ $ 0.025829 $\ \ \ \ \ \ $ 84.202 $\ \ \ \ $ [0.0000] $\ \ \ $ 49.824 $\ \ \ $ [0.0000]
2 $\ \ \ \ \ \ \ $ 0.016353 $\ \ \ \ \ \ $ 34.378 $\ \ \ \ $ [0.0000] $\ \ \ $ 31.393 $\ \ \ $ [0.0000]
3 $\ \ \ \ \ \ \ $ 0.0015664 $\ \ \ \ $ 2.9847 $\ \ \ \ $ [0.0841] $\ \ \ $ 2.9847 $\ \ \ $ [0.0841]

can anyone kindly help me in interpreting these results? I have conducted a Johansen's co-integration test for a commodity series with respect to the futures.

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When looking at the gretl user's guide (p. 241ff.) it can be seen that you can reject the null hypothesis of r = 0, r <= 1, ..., r<=3, although the last one only at the 10% significance level. So only based on these results you can assume that there exists a cointegration relation between these time series. Although you probably need some theoretical backup for this hypothesis.

Perhaps also take a look at some text book on the application of the Johansen procedure. One nice example is "Cointegration for the Applied Economist", Second Edition by B. Bhaskara Rao.

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Assuming you are showing the complete test output you seem to have included 4 variables (series) in your test, and from your description I'm guessing that it's one spot price series and three different futures prices.

The way to read this is from top to bottom (this is not gretl-specific), so the conclusion of the test sequence is either r=3 or r=4, depending on your significance level. (Also abstracting from potential small-sample issues, since you haven't shown the sample size.) The case r=4 would mean that each of the 4 series is stationary (relative to the included deterministic terms that you haven't shown, either), which may or may not be a reasonable outcome. The case r=3 would mean that there are 3 (linearly independent) cointegration relationships, not just one.

A natural follow-up hypothesis after r=3 would be that for any series pair x,y the difference x-y would be I(0), so the matrix of cointegration vectors could be written as a 3-dim identity matrix on top with a fourth bottom row of (-1, -1, -1). But this does not follow from the pure Johansen test results, the unit coefficients are just a reasonable theoretical possibility (which can be tested in gretl).

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