Interpreting Johansen Trace Test Results for Two Series

Summary

The document asks how to interpret MATLAB output from a Johansen trace test applied to two series. It shows results for the hypotheses associated with cointegration rank zero and rank one, including trace statistics, critical values, p-values, and a decision table. The accepted response interprets the rank-zero result as a failure to reject no cointegration and the rank-one result as a rejection at the 5% level, then concludes that the series are not cointegrated.

That conclusion needs care: Johansen rank tests are typically read sequentially, beginning with the null of rank zero and moving to higher ranks only if that null is rejected. Since the shown rank-zero test is not rejected, the sequential interpretation supports rank zero; the later rank-one result does not override that first decision. The response suggests checking additional ranks, but the excerpt does not explain model specification, lag selection, or other assumptions that affect inference.

Key ideas

• The Johansen trace test evaluates hypotheses about the cointegration rank of a set of series.
• The displayed rank-zero result has a p-value above the stated 5% significance level and does not reject rank zero.
• Rank tests are generally interpreted sequentially, so a first failure to reject is the key stopping point.
• Inference also depends on model and lag choices, which the excerpt does not discuss.

Tags

# matlab interpretation of johansen cointegration test


# matlab interpretation of johansen cointegration test












I need some help understanding the results of Johansen Cointegration test run on MATLAB. I am quite new to econometrics and do not fully comprehend what MATLAB has come up with. I would be really in debt if someone could explain the following in layman terms.

The test was run on two series.

```
Data: Y
Effective sample size: 1871
Model: H1
Lags: 0
Statistic: trace
Significance level: 0.05

r  h  stat      cValue   pValue   eigVal   
========================================
0  0  11.0750   15.4948  0.2115   0.0037  
1  1  4.2114    3.8415   0.0402   0.0022
```

h =

```
      r0       r1   
t1    false    true
```

pValue =

```
      r0         r1      
t1    0.21149    0.040163
```

## Answer by Quantopik (score 1, accepted)

https://quant.stackexchange.com/a/17256

The test fails to reject the null hypothesis of no cointegration since the p-value for `r0` is greater than 0.10, and, instead, it rejects the null hypothesis of 1° rank cointegration `r1` at 5.0 % level of significance (since the p-value is 4.01 %).

So, looking at the test results, the series are not cointegrated, although I suggest to check for higher ranks and level of cointegration (`r2`, `r3`,...).

You can find more references about the test on mathworks and on the quant.stackexchange site about the Johansen interpretation test in R.

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