Hatemi-J Cointegration Test with Two Regime Shifts
Also known as: Hatemi-J Test, Two-Break Cointegration Test, Cointegration Test with Two Regime Shifts, Hatemi-J İki Kırılmalı Eşbütünleşme Testi
The Hatemi-J cointegration test, introduced by Abdulnasser Hatemi-J in 2008, tests for a long-run equilibrium relationship between integrated time series while allowing for up to two unknown structural breaks in the cointegrating vector. It extends earlier single-break approaches by permitting both the intercept and slope coefficients of the cointegrating regression to shift at two endogenously determined breakpoints, making it particularly suited for economic and financial data spanning periods of major institutional or policy change.
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When to use it
Use the Hatemi-J test when you suspect a long-run relationship between I(1) variables but also believe the relationship may have shifted twice due to structural events such as financial crises, monetary unions, or trade liberalizations. The test requires at least roughly 60–80 observations to support reliable grid search and sub-sample estimation. It assumes that no more than two breaks occur and that variables are integrated of order one. If only one break is expected, the Gregory-Hansen test is more parsimonious. For tests that also account for structural breaks in the unit-root null, the Lee-Strazicich test is an alternative.
Strengths & limitations
- Allows for two endogenous structural breaks in both the intercept and slope of the cointegrating vector, capturing more complex real-world dynamics than single-break alternatives.
- Provides both ADF-type and Phillips-Perron-type test statistics, offering robustness to serial correlation and heteroskedasticity in residuals.
- Break dates are determined from the data rather than imposed a priori, reducing specification error.
- Applicable to bivariate and multivariate cointegrating systems with multiple regressors.
- Critical values are simulation-based and depend on the number of regressors; using wrong table entries leads to invalid inference.
- The grid search is computationally intensive and grows quadratically with sample size when two breaks are considered.
- The test assumes at most two structural breaks; undetected additional breaks inflate the null rejection rate.
- Small samples reduce the power of the test and the precision of break-date estimates significantly.
Frequently asked
How does the Hatemi-J test differ from the Gregory-Hansen test?
The Gregory-Hansen (1996) test allows for only one unknown structural break in the cointegrating vector, while the Hatemi-J (2008) test generalizes this to two unknown breaks. When two breaks are present and a single-break test is applied, the latter may fail to detect cointegration because the single estimated break cannot absorb both structural shifts, reducing power. The Hatemi-J test uses a two-dimensional grid search and different critical values to accommodate this more general scenario.
What model variants does the Hatemi-J test offer?
Following the Gregory-Hansen convention, the Hatemi-J test offers three model variants: a level-shift model where only the intercept changes at the break dates, a level-shift with trend model that also allows a trend break, and a regime-shift model where both the intercept and all slope coefficients are permitted to change at the two break dates. The regime-shift model is the most general and appropriate when the long-run relationship itself is expected to change structurally.
Can the Hatemi-J test be applied to multivariate systems with more than one regressor?
Yes. The cointegrating regression can include multiple I(1) regressors, each interacted with the two regime-shift dummies in the full regime-shift model. However, the critical values provided by Hatemi-J (2008) are tabulated for different numbers of regressors, so the researcher must use the correct column from the critical-value tables corresponding to the actual dimension of the cointegrating regression.
Sources
- Hatemi-J, A. (2008). Tests for cointegration with two unknown regime shifts with an application to financial market integration. Empirical Economics, 35(3), 497–505. DOI: 10.1007/s00181-007-0175-9 ↗
How to cite this page
ScholarGate. (2026, June 2). Hatemi-J Cointegration Test with Two Regime Shifts. ScholarGate. https://scholargate.app/en/econometrics/hatemi-j-cointegration-test
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