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Econometrics and Financial Time Series / Nonstationarity, Unit Roots, and Cointegration

The Johansen Procedure for Multiple Cointegrating Vectors

A curve of yields or a basket of related securities can contain several independent long-run restrictions. Single-equation Engle--Granger finds at most one and forces an arbitrary normalisation. Johansen estimates the whole system as a VECM and tests the number of stationary combinations.
Learning objectives. By the end of this note you should be able to:
  • interpret the rank of the VECM long-run matrix;
  • state trace and maximum-eigenvalue rank tests;
  • factor Π=αβ′\boldsymbol\Pi=\boldsymbol\alpha\boldsymbol\beta';
  • execute the sequential rank-selection workflow.

In this lesson

  1. Rank is the number of equilibria
  2. What to report

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