Interpreting Johansen Cointegration Tests for Oil and Corn Prices

Summary

The document presents a question about applying the Johansen procedure to oil and corn price series after unit-root tests suggest both are nonstationary. It shows example eigenvalue and trace test statistics alongside critical values, then asks how to interpret the sequential rank hypotheses and what the results imply about cointegration.

It also raises a separate modeling question: whether finding one cointegrating relationship identifies one price as dependent. The document contains no response or conclusion, so it does not resolve the test interpretation or select a dependent variable. In general, Johansen tests assess the rank of the system's cointegration space; a single relation does not by itself establish a unique causal or dependent price. Interpretation also depends on choices such as deterministic terms and lag specification, which are not described here.

Key ideas

• The Johansen procedure tests the cointegration rank of a multivariate price system.
• Eigenvalue and trace tests use sequential null hypotheses about the number of cointegrating relations.
• The example concerns oil and corn prices already assessed as nonstationary.
• A finding of one cointegrating relation does not alone identify a dependent price or causal direction.
• The document omits model specifications and does not supply an interpretation of its reported statistics.

Tags

# Johansen Cointegration Test in R


# Johansen Cointegration Test in R












I know its probably been asked bevor but i just don't get it. I have 2 values (Oil and corn price) and i want to check if they are cointegrated. Bevor that, i have tested if they really are non stationarity (and they are assuming to ADF,KPSS and PP).

## Eigen Test

The value of the test statistic is: 3.17 10.9942

```
              10pct  5pct  1pct
     r <= 1 |  7.52  9.24 12.97
     r = 0  | 13.75 15.67 20.20
```

The first test stats say that: $H_0$ should be that there is no cointegration at all, but:

10.9942 < 15.67 --> $H_0$ to be rejected -> cointegration exists.

What does the second line say?

## Trace Test

The value of the test statistic is: 3.17 14.1641

```
              10pct  5pct  1pct
     r <= 1 |  7.52  9.24 12.97
     r = 0  | 17.85 19.96 24.60
```

What does this test tell me? Where is the difference? If i know that there is one cointegration, which one is the dependent one?

I appreciate your help!

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.