This paper proposes an endogenous two-break Lagrange multiplier (LM) unit root test that allows for breaks under both the null and alternative hypotheses. The test is designed to unambiguously imply trend stationarity upon rejection of the null hypothesis. The test is based on the LM unit root test initially suggested by Schmidt and Phillips (1992). Unlike the LP test, which assumes no breaks under the null hypothesis, the LM test does not require this assumption, as its distribution is invariant to breakpoint nuisance parameters. The test is extended to allow for two structural breaks, and the test statistics are derived under the assumption that the data-generating process includes breaks under both the null and alternative hypotheses.
The paper discusses the asymptotic properties of the endogenous two-break LM unit root test, examines its performance in simulations, and applies it to Nelson and Plosser's (1982) data. The results show that the two-break LM test performs well in the presence of breaks under the null hypothesis and is robust to their misspecification. In contrast, the LP test exhibits significant rejections in the presence of breaks under the null hypothesis, which can be interpreted as either high power when the alternative hypothesis is "structural breaks are present" or as spurious rejections when the null includes a unit root with breaks.
The paper also compares the two-break LM test with the LP test in terms of their ability to detect trend stationarity. The results show that the two-break LM test provides a more accurate assessment of trend stationarity, as it unambiguously implies trend stationarity upon rejection of the null hypothesis. The paper concludes that the two-break LM test is a more robust and reliable test for detecting trend stationarity in the presence of structural breaks.This paper proposes an endogenous two-break Lagrange multiplier (LM) unit root test that allows for breaks under both the null and alternative hypotheses. The test is designed to unambiguously imply trend stationarity upon rejection of the null hypothesis. The test is based on the LM unit root test initially suggested by Schmidt and Phillips (1992). Unlike the LP test, which assumes no breaks under the null hypothesis, the LM test does not require this assumption, as its distribution is invariant to breakpoint nuisance parameters. The test is extended to allow for two structural breaks, and the test statistics are derived under the assumption that the data-generating process includes breaks under both the null and alternative hypotheses.
The paper discusses the asymptotic properties of the endogenous two-break LM unit root test, examines its performance in simulations, and applies it to Nelson and Plosser's (1982) data. The results show that the two-break LM test performs well in the presence of breaks under the null hypothesis and is robust to their misspecification. In contrast, the LP test exhibits significant rejections in the presence of breaks under the null hypothesis, which can be interpreted as either high power when the alternative hypothesis is "structural breaks are present" or as spurious rejections when the null includes a unit root with breaks.
The paper also compares the two-break LM test with the LP test in terms of their ability to detect trend stationarity. The results show that the two-break LM test provides a more accurate assessment of trend stationarity, as it unambiguously implies trend stationarity upon rejection of the null hypothesis. The paper concludes that the two-break LM test is a more robust and reliable test for detecting trend stationarity in the presence of structural breaks.