Lee-Strazicich LM Unit-Root Test with Two Structural Breaks
Lee-Strazicich LM Unit-Root Test with Two Breaks · Also known as: LS Unit Root Test, Minimum LM Unit Root Test, Lee-Strazicich Two-Break Test, Lee-Strazicich LM Testi
The Lee-Strazicich (2003) test is a Lagrange Multiplier-based unit-root test that allows for two endogenous structural breaks under both the null and alternative hypotheses. Proposed by Junsoo Lee and Mark C. Strazicich, it corrects a fundamental flaw in earlier break-based tests such as Zivot-Andrews, where structural breaks were permitted only under the alternative. By incorporating breaks under the null, the LS test avoids spurious rejections and provides size-correct inference in the presence of level or trend shifts.
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When to use it
Use the Lee-Strazicich test when you suspect a time series has undergone up to two structural breaks in its level or trend—common in macroeconomic and financial series spanning policy changes, crises, or regime shifts. The test requires a single univariate series observed at equal time intervals and works best with samples of at least 50–100 observations. It is appropriate when prior tests such as ADF or KPSS gave ambiguous results or when economic reasoning suggests breaks exist. It is not suited for panel data, seasonal series without prior adjustment, or situations requiring more than two breaks, for which the Carrion-i-Silvestre et al. panel break tests or the Bai-Perron multiple-break framework are preferable alternatives.
Strengths & limitations
- Allows structural breaks under both null and alternative, eliminating spurious rejections that plague earlier break-based tests
- Break dates are selected endogenously via grid search, requiring no prior knowledge of when breaks occurred
- Handles two simultaneous breaks—more flexible than single-break tests like Zivot-Andrews while remaining parsimonious
- LM principle ensures nuisance-parameter-free critical values that depend only on break fraction locations
- Critical values are tabulated for two breaks; generalising to one or three breaks requires different tables or simulation
- Grid search is computationally intensive for long series, though manageable with modern software
- Power can be low in small samples, particularly when true break magnitudes are modest
- Does not account for nonlinear adjustment or smooth breaks; smooth-transition unit-root tests may be preferable in such cases
Frequently asked
How does the Lee-Strazicich test differ from the Zivot-Andrews test?
Zivot-Andrews allows a structural break only under the alternative hypothesis of stationarity. If a break also exists under the unit-root null, this causes the test to reject the null too frequently even when the series is nonstationary. The Lee-Strazicich test allows breaks under both null and alternative via the LM principle, so its rejection is genuinely informative. It also accommodates two breaks versus the single break of Zivot-Andrews.
Which model should I choose—Model A or Model C?
Model A allows for breaks in the level (intercept) only, appropriate when the trend slope is assumed unchanged. Model C allows breaks in both level and trend slope, which is more flexible but uses additional degrees of freedom. Choose based on economic reasoning: if a policy event plausibly changed both the mean and growth rate of the series, use Model C; for pure level shifts, Model A suffices. Using the wrong model yields incorrect critical values.
How many observations do I need for the test to be reliable?
Lee and Strazicich (2003) derive asymptotic critical values, so performance depends on sample size. Simulation studies suggest at least 50 observations for acceptable size control, with 100 or more preferred when two breaks are estimated simultaneously. In small samples, the grid search leaves few interior observations per sub-period, inflating variance of the break-date estimator and reducing power against stationary alternatives with moderate break sizes.
Sources
- Lee, J., & Strazicich, M. C. (2003). Minimum Lagrange multiplier unit root test with two structural breaks. Review of Economics and Statistics, 85(4), 1082–1089. DOI: 10.1162/003465303772815961 ↗
How to cite this page
ScholarGate. (2026, June 2). Lee-Strazicich LM Unit-Root Test with Two Breaks. ScholarGate. https://scholargate.app/en/econometrics/lee-strazicich-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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