Cointegration and Error Correction

Two asset prices may each drift while a particular combination remains stable. That combination can support an equilibrium-error model for a spot–futures basis or a candidate pairs spread. This lesson tests the combination, explains error-correction dynamics, and extends the analysis to several equilibria with Johansen rank tests. Stationarity of a spread still does not establish profitable trading after costs or stability in a later regime.

• define cointegration and execute Engle–Granger with correct residual critical values;
• write and interpret a bivariate ECM (short-run vs adjustment speed);
• interpret Johansen rank, $\boldsymbol\Pi=\boldsymbol\alpha\boldsymbol\beta'$, and sequential trace/max-eigenvalue testing;
• connect a tested spot–futures or equity-pair relation to an implementable spread model without claiming profitability.

1. Cointegration
2. Engle–Granger two-step
3. Error-correction models
4. Johansen (multiple vectors)
5. Spot–futures and pairs bridge