Engle-Granger Cointegration Test

The Engle-Granger cointegration test regresses one integrated series on another and applies a unit root test to the residuals to decide whether a stationary long-run equilibrium links them.

Engle-Granger 공적분 검정은 적분된 한 시계열을 다른 시계열에 회귀한 뒤 잔차에 단위근 검정을 적용해 둘 사이에 정상적인 장기 균형 관계가 있는지 판단한다.

Do house prices and household income move together in the long run, or is their correlation spurious?

주택가격과 가구소득이 장기적으로 함께 움직이는지, 아니면 겉보기 상관인지 확인하고 싶어요.

The test first estimates the cointegrating regression by ordinary least squares and then runs an ADF-type test on its residuals. If the residuals are stationary, judged against MacKinnon critical values rather than standard ADF tables, the two series are cointegrated.

When to use Engle-Granger Cointegration Test

• Both series are integrated of order one.
• You want to test for a single long-run relation between two series.
• You plan an error-correction model if cointegration holds.

When to use something else

• There are three or more series that may have several cointegrating relations; use the Johansen procedure or a Vector Error Correction Model (VECM).
• The integration order of the regressors is unknown or mixed; use the ARDL bounds approach.

Assumptions and requirements

• Each series is I(1).
• At most one cointegrating vector.
• Residual dynamics captured by the lag augmentation.
• Only the first feature is used as the second series.

What the analysis reports

• Engle-Granger τ statistic and MacKinnon p-value
• Critical values at 1%, 5% and 10%
• Cointegrating regression intercept and slope
• R² of the cointegrating regression

How to report it

An Engle-Granger test gave τ = [value], p = [value]; the cointegrating regression was y = [value] + [value]x.

Related methods

• Vector Error Correction Model (VECM)
• Phillips-Perron Unit Root Test
• Autoregressive Distributed Lag Model (ARDL)

Run Engle-Granger Cointegration Test on Quorant