Gregory-Hansen Cointegration Test with Regime Shift
Also known as: GH Cointegration Test, Gregory-Hansen Regime Shift Test, Residual-Based Cointegration Test with Structural Break, Rejim Değişimli Koentegrasyon Testi
The Gregory-Hansen test, introduced by Allan Gregory and Bruce Hansen in 1996, extends the standard Engle-Granger cointegration framework to allow for a single unknown structural break in the cointegrating relationship. It is designed for researchers who suspect that the long-run equilibrium between integrated variables may have shifted at some point during the sample period, and who wish to test for cointegration without presupposing the break date.
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When to use it
Use the Gregory-Hansen test when you have two or more I(1) time series and theoretical or historical grounds to believe the cointegrating relationship may have shifted once during the sample — for example, around a major policy change, a currency crisis, or a regime transition. The test is appropriate when the break date is unknown and must be estimated from the data. It assumes at most one structural break; if multiple breaks are suspected, consider the Hatemi-J test or other multi-break alternatives. The series must be integrated of order one, and the sample should be large enough (typically T > 50) for reliable inference. It is not suited for stationary series or for detecting breaks in the short-run dynamics rather than the long-run level.
Strengths & limitations
- Allows for an unknown structural break date, making it robust to common misspecification in standard cointegration tests
- Offers three flexible model specifications (C, C/T, C/S) to accommodate different forms of regime shift
- Provides three complementary test statistics (ADF*, Zt*, Za*), enhancing robustness of inference
- Directly estimates the most likely break date as a by-product of the testing procedure
- Restricted to a single structural break; cannot detect multiple regime shifts without modification
- Requires relatively large samples for the asymptotic critical values to be reliable
- The infimum-based approach can over-reject the null in small samples due to the search over many break dates
- Assumes both variables are I(1); pre-testing with unit root tests is necessary and introduces pre-test bias
Frequently asked
How does the Gregory-Hansen test differ from the standard Engle-Granger test?
The Engle-Granger test assumes the cointegrating vector is constant over the entire sample and uses a fixed OLS regression to obtain residuals. The Gregory-Hansen test augments that regression with a structural break dummy at each possible date, selects the date that minimizes the ADF statistic, and applies critical values corrected for the break-search procedure. This makes it valid — unlike Engle-Granger — when a one-time regime shift may have occurred.
Which of the three models (C, C/T, C/S) should I choose?
Model C (level shift) allows only the intercept to shift and suits cases where the equilibrium level changes but the slope is stable. Model C/T adds a deterministic trend and is appropriate when the series exhibit trending behaviour around the break. Model C/S (regime shift) allows both the intercept and slope to change and is the most general; it is preferred when theory suggests the speed of adjustment or the equilibrium ratio may itself have changed. Reporting all three is common in practice.
What should I do if the Gregory-Hansen test rejects the null but the Engle-Granger test does not?
This pattern suggests the long-run relationship exists but is subject to a structural break that the standard test cannot accommodate. You should report the estimated break date from the Gregory-Hansen procedure, examine whether it corresponds to a plausible economic event, and proceed with a cointegrating model that incorporates the break — for example, an error-correction model with a break dummy — to accurately capture the adjustment dynamics.
Sources
- Gregory, A. W., & Hansen, B. E. (1996). Residual-based tests for cointegration in models with regime shifts. Journal of Econometrics, 70(1), 99–126. DOI: 10.1016/0304-4076(69)41685-7 ↗
How to cite this page
ScholarGate. (2026, June 2). Gregory-Hansen Cointegration Test with Regime Shift. ScholarGate. https://scholargate.app/en/econometrics/gregory-hansen-test
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
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