Cointegration is an analytic technique for testing for common trends in multivariate time series and modeling long-run and short-run dynamics. Two or more predictive variables in a time-series model are cointegrated when they share a common stochastic drift. Variables are considered cointegrated if a linear combination of them produces a stationary time series.

The Engel-Granger method tests for individual cointegrating relationships and estimates their parameters. Johansen methods test for multiple cointegrating relationships, and estimate parameters in corresponding vector error-correction (VEC) models. In addition, Johansen methods test linear restrictions on both error-correction speeds and the space of cointegrating vectors, and estimate restricted model parameters.

Cointegration models are used by financial institutions to develop statistical arbitrage trading strategies. You can perform cointegration analysis with Econometrics Toolbox™, which provides Engle-Granger and Johansen methods for testing and modeling.