Minimum Lagrange Multiplier Unit Root Test with Two Structural Breaks

TLDR

The Lumsdaine–Papell two‑break unit root test assumes no structural breaks under the null, so rejecting the null may signal a unit root without break, while the alternative may indicate a unit root with breaks rather than trend stationarity. This paper proposes an endogenous two‑break Lagrange multiplier unit root test that permits structural breaks under both the null and alternative hypotheses. The test extends the Lumsdaine–Papell framework by incorporating a Lagrange multiplier statistic that accommodates two endogenous breaks in the series. Rejection of the null unambiguously indicates trend stationarity.

Abstract

The endogenous two-break unit root test of Lumsdaine and Papell is derived assuming no structural breaks under the null. Thus, rejection of the null does not necessarily imply rejection of a unit root per se, but may imply rejection of a unit root without break. Similarly, the alternative does not necessarily imply trend stationarity with breaks, but may indicate a unit root with breaks. In this paper, we propose an endogenous two-break Lagrange multiplier unit root test that allows for breaks under both the null and alternative hypotheses. As a result, rejection of the null unambiguously implies trend stationarity.