2.Banerjee, A., Lumsdaine R. L. and J. H. Stock (1992)“Recursive and sequential tests of the unit-root and trend break hypotheses:theory and international evidence”, Journal of Business and EconomicStatistics, 10, 271-287

Banerjee, Lumsdaine and Stock(1992) use various recursive and sequential tests which endogenise thebreakpoint. They consider the recursive maximum and minimum DF test and thedifference between them deriving the asymptotic distribution of the recursiveand sequential test statistics and tabulating the relative critical values.

3.Perron, P. (1989)“The great crash, the oil-price shock and the unit root hypothesis”, Econometrica,57, 1361-1401

Perron (1989) first showed theimportance of such tests, arguing that if there is a break in the deterministictrend, unit root tests tend to under-reject the null of a unit root. Taking thebreakpoint as exogenous, he suggests a modification of the Dickey-Fuller testwith three different types of deterministic trend functions. These allow, inturn, for a one-off change in the intercept, a change in slope of the trend,and both of them. The null of a unit root is then tested against thealternative of a broken trend stationary. After Perron’s (1989) seminal paperseveral testing methods have been developed where the break point is assumed tobe unknown. This is often referred to as an endogenous breakpoint. Theseprocedures comprise recursive (using sub-samples), rolling (using a fixed-sizewindow that moves along the sample), and sequential methods (includingswitching dummies in the full sample).

4.Zivot , E. and D.W.K. Andrews (1992) “Further evidence onthe great crash, the oil-price shock and he unit root hypothesis”, Journalof Business and Economic Statistics, 10, 251-270

Zivot and Andrews (1992) use asequential unit root test, derive its distribution, and tabulate its criticalvalues.

5.Lumsdaine R. L. and D. H. Papell (1997) “Multiple trendbreaks and the unit root hypothesis”, Review of Economics and Statistics,79, 212-218

Lumsdaine and Papell (1997)extend the analysis to the case of multiple breaks with unknown breakpoints.

6.Gregory, A. W., Nason, J. M. and D. Watt (1996) “Testingfor structural breaks in cointegrated relationships”, Journal ofEconometrics, 71, 324-341

Gregory, Nason and Watt (1996)study the sensitivity of the ADF test for cointegration in the presence of asingle permanent break. Using Monte Carlomethods they show that the presence of a break results in under-rejection ofthe null of no cointegration implying the inappropriateness of constantparameter cointegration analysis in such cases.

7.Hansen B. E., (1992) “Tests for parameter instability inregressions with I(1) processes”, Journal of Business and EconomicStatistics, 10, 321-335

Hansen (1992) derives theasymptotic distribution of a LM test for parameter instability against severalalternatives in the context of cointegrated regression models.

8.Gregory, A. and B. E. Hansen, (1996) “Residual –basedtests for cointegration in models with regime shifts”, Journal ofEconometrics, 70, 99-126

Gregory and Hansen (1996) proposeseveral tests for the null of no cointegration against the alternative ofcointegration in the presence of a possible break in the intercept or the slopecoefficients in the cointegrating relation at an unknown point in time.

9.Seo, B. (1998)“Tests for structural change in cointegrated systems” Econometric Theory,14, 222-259

Seo (1998) defines LM tests statistics for structuralchanges in both the cointegrating vector and the vector of adjustmentparameters for both the cases of a known and unknown breakpoint. Using Monte Carlo methods he finds that the tests forstructural change of the cointegrating vector have a non-standard distributionthat is equal to the one found by Hansen (1992) using the FM technique.

10.VOGELSANG, T. J. (1997) Wald-typetests for detecting breaks in the trend function of a dynamic time series,Econometric Theory, 13: 818-849.

11.PERRON, P., T. J. VOGELSANG. (1993)Testing for a Unit Root in a Time Series with a Shift in Mean: Corrections andExtensions. Journal of Business and Economic Statistics, 10: 467-470.

12.PERRON, P., T. J. VOGELSANG. (1998)Additional Tests for Unit Root Allowing the Possibilityof Breaks in the TrendFunction. International Economic Review, 39: 1073-110.

We consider unit root tests that allowa shift in trend at an unknown time. We focus on the additive outlier approach,but also give results for the innovational outlier approach. Various methods ofchoosing the break date are considered. New limiting distributions are derived,including the case where a shift in trend occurs under the unit root nullhypothesis. Limiting distributions are invariant to mean shifts but not toslope shifts. Simulations are used to assess finite sample size and power. We focuson the effects of a break under the null and the choice of break date.

13.PERRON, P., G. RODRIGUEZ.(2003) GLS detrending, efficient unit root tests and structural change. Journalof Econometrics, 115:1-27.

We extend the class of M-tests for a unit root analyzed by Perron and Ng (Rev.Econ. Studies63(1996)435)and Ng and Perron (Econometrica 69 (2001)1519)to the case whereachange in the trend function is allowed to occur at an unknown time.Thesetests (M GLS )adoptthe GLSdetrending approach developed by Elliott etal.(Econometrica 64 (1996)813)(ERS) following the results of Dufour and King(J.Econometrics 47 (1991)115).Following Perron (Econometrica 57 (1989)1361),weconsider two models:one allowing for a change in slope and the other for both achange in intercept and slope.We derive the asymptotic distributions of thetests as well as that of the feasible point optimal test (P GLS )suggested byERS.Also, we compute the non-centrality parameter used for the local GLSdetrendingthat permits the test P GLS T to have 50%asymptotic power at that value.The asymptoticcritical values of the tests are tabulated.We show that the M GLS and P GLS Ttests have an asymptotic power function close to the power envelope.Asimulation study analyzes the size and power in nite samples under variousmethods to select the truncation lag for the autoregressive spectral

density estimator.Anempirical application is also provided.

14.PERRON, P. (1997) Further evidenceon breaking trend functions in macroeconomic variables.Journal of Econometrics,80: 355-385.

This study first reexamines thefindings of Perron (1989) regarding the claim that most macroeconomic timeseries are best construed as stationary fluctuations around a deterministictrend function if allowance is made for the possibility of a shift in theintercept of the trend function in 1929 (a crash) and a shift in slope in 1973(a slowdown in growth). Unlike that previous study, the date of possible changeis not fixed a priori but is considered as unknown. We consider various methodsto select the break points and the asymptotic and finite sample distributionsof the corresponding statistics. A

detailed discussion about the choice ofthe truncation lag parameter in the autoregression and of its effect on thecritical values is also included. Most of the rejections reported in Perron(1989) are confirmed using this approach. Secondly, this paper investigates aninternational data set of post-war quarterly real GNP (or GDP) series for theG-7 countries. Our results are compared and contrasted to those of Banerjee etal. (1992) and Zivot and Andrews (1992). In contrast to the theoretical resultscontained in these papers, we derive the limiting distribution of thesequential test without trimming.