Cointegration as a Long-Run Relationship Between Nonstationary Series
Summary
The document introduces cointegration as a way to model related time series that are individually nonstationary. If a linear combination of such series is stationary, that combination represents a stable long-run relationship, even though the component series may drift. Short-term disturbances can move the variables away from their balance; cointegration implies those deviations are temporary in the modeled relationship. The text uses consumption and income as an illustrative economic example.
It gives the formal definition: a vector of series is cointegrated when its components share an integration order and a nonzero linear combination has a lower order of integration. For a two-variable test, it recommends first checking stationarity with a unit-root test such as ADF. The discussion is conceptual rather than empirical: it supplies no market data, trading rules, or backtest results. Its stated same-order condition is specifically qualified for the bivariate case and does not generally cover multivariate cointegration.
Key ideas
- Individually nonstationary series can have a stationary linear combination.
- That stationary combination can represent a long-run equilibrium relationship.
- Cointegration is defined through shared integration order and a lower-order linear combination.
- For two series, the document recommends checking for unit roots before testing cointegration.
- The explanation offers no trading strategy or empirical performance evidence.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.