Using the Johansen Test to Find Multivariate Cointegration
Summary
The document introduces the Johansen cointegration test as a way to assess long-run relationships among several time series. It explains that the trace and maximum eigenvalue tests use eigenvalues to estimate the number of cointegrating relationships, and contrasts this multivariate approach with the Augmented Dickey-Fuller test. A stationary combination of asset prices may support mean-reversion strategies such as pairs trading or trading portfolios with more than two assets.
A Python example applies the test to three pairs of large US stocks. It compares trace statistics with critical values for the null of no cointegrating relationships and describes how the decision depends on the hypothesis being tested. The document’s reported pair-level classifications conflict with its earlier interpretation of the trace statistics, so its example should be treated cautiously. It offers little detail on model specification, data choices, or out-of-sample validation, and a statistical finding alone does not establish a profitable trading strategy.
Key ideas
- The Johansen test assesses cointegrating relationships among multiple time series.
- Trace and maximum eigenvalue tests help estimate the number of such relationships.
- A stationary combination of asset prices can be considered for mean-reversion trading.
- Critical values must be matched to the specific null hypothesis being tested.
- The article’s example gives inconsistent interpretations, and cointegration alone does not establish profitability.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.