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Cointegration

Cointegration occurs when two or more nonstationary time series have a linear combination that is stationary. In simpler terms, although the prices of two assets move in a non-stationary (trend) manner, their "distance" or relationship tends to remain stable over time.

Above, two asset prices that both trend upward. Below, the spread between them, which keeps oscillating around a stable mean within two standard deviations.
Two trending prices are cointegrated when the distance between them stays stationary.

One of the ways to test for cointegration is the Engle-Granger test.

Steps of the Engle-Granger Test: first, a linear regression is performed between the two assets; a unit root test is applied to the residuals: if the residuals are stationary, it means the series are cointegrated.

If the p-value < 0.05: the residuals are stationary and therefore the two series are cointegrated.

If p-value > 0.05: the residuals are not stationary and the two series are not cointegrated.

Some things to consider: cointegrating relationship may change over time; requires a long enough time horizon; cointegrated assets may offer hedging opportunities; when moving away from the average relationship there may be trading opportunities.

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