Interpreting Johansen and Engle–Granger Cointegration Test Results
Summary
The document explains how to read output from Johansen and Engle–Granger cointegration tests for a pair of time series. In the example, the test indicators fail to reject their null hypotheses, and the reported p-values are high. The answer interprets this as evidence that the pair has not been shown to be cointegrated, correcting the questioner’s conclusion that a high p-value indicates a significant relationship.
The discussion presents low p-values and test statistics that meet the relevant critical-value threshold as reasons to investigate cointegration further. It also notes that each Engle–Granger output contains results for two test specifications. These test results alone do not establish that a pair is suitable for forecasting or trading: the post provides no follow-up diagnostics, stability analysis, or out-of-sample evidence, and statistical test conclusions depend on the test setup and assumptions.
Key ideas
- Failure to reject the null in these tests means the example does not establish cointegration.
- A high p-value is not evidence in favor of a cointegrating relationship.
- The Engle–Granger output shown reports results for two test specifications.
- Test statistics should be assessed against the relevant critical values as well as p-values.
- Cointegration test output alone does not demonstrate forecasting or trading performance.
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Full text
# Cointegration results interpretation validation?
# Cointegration results interpretation validation?
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
## Answer by SolitonK (score 2, accepted)
https://quant.stackexchange.com/a/15598
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:
- 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.
- 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.
- 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.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.