Since the publication of the influential papers by Rap- poport and Reichlin (1989) and Perron (1989), which provide evidence that many macroeconomic time series might best be modeled as stationary around a broken trend, the detection of structural change in the trend func- tion of a time series has captured the attention of econo- metricians and applied researchers. Much of the subse- quent research has focused on testing the unit root hy- pothesis in the presence of one time structural change where the date of structural change may or may not be known. Contributions in this area include Christiano (1992), Banerjee, Lumsdaine and Stock (1992), Zivot and Andrews (1992), Perron (1997) and Perron and Vogelsang (1998). Perron (1994) and Maddala and Kim (1996a) pro- vide useful summaries. In related work, Vogelsang (1997) develops tests for a change in trend that are robust to whether the data are or thereby extending the results of Andrews (1993) to some models with trending data. Empirically, the unit root hypothesis has been re- jected in favor of a broken trend model with one change for numerous series. Most notably, using various tech- niques and tests, the unit root hypothesis has been re- jected for many international output series by Banerjee et al. (1992), Raj (1992), Perron (1992), De Haan and Zel- horst (1993), Zelhorst and De Haan (1995), Cheung and Chinn (1996), Ben-David and Papell (1995) and Perron (1997). Unit roots have been rejected in favor of a single trend break model for several inflation series by Evans and Lewis (1995) and Culver and Papell (1997), for real exchange rates by Edison and Fisher (1991), Perron and Vogelsang (1992) and Culver and Papell (1995), and for real interest rates by Perron (1990). Overall, there is a large body of evidence to suggest that the trend function of many macroeconomic time series can be modeled as de- terministic with at least one structural change. A natural extension of the literature on testing for unit roots in the presence of structural change involves allow- ing for more than one possible break date under the alter- native broken trend stationary model. Indeed, for many macroeconomic time series for which the possibility of structural change is entertained the assumption of at most one break date is unrealistic and restrictive. For exam- ple, trend breaks are often motivated by “big events” like wars, oil price shocks, financial crisis or changes in politi- cal or institutional regimes and most long time series con- tain several such events. To this end, Lumsdaine and Pa- pell (1997) extend the Zivot-Andrews (1992) testing pro- cedure to allow for up to two possible endogenous breaks and they find more evidence against the unit root hypoth- esis than Zivot and Andrews, but less than Perron (1997). Ben-David, Lumsdaine and Papell (1997) find further ev- idence for at least two structural breaks for three quarters of the per capita real GDP series collected by Maddison (1995). In addition, Papell (1998) finds evidence of mul- tiple breaks in numerous European real exchange rates, Kanas (1998) finds evidence for up to six breaks in ERM exchange rates and Garcia and Perron (1996) find evi- dence for two breaks in U.S. real interest rates. Indeed, there is a growing body of results that support trend sta- tionary models with multiple breaks for many macroeco- nomic and financial time series. In addition to changes in level and trend, changes in variance are often found in economic and financial data. For example, Schwert (1990) finds that the stock mar- ket volatility is higher during and after the 1987 crash, compared with other periods. Incl´ an (1993), Incl´ an and Tiao (1994) and Chen and Gupta (1997) detect multiple changes in variance for various series of stock returns. Lamoureux and Lastrapes (1990) suggest that the empir- ical persistence of volatility captured by GARCH models might be caused by structural changes in variance and this view has been supported by Wilson, Aggarwal and Incl´ an (1996) and Fong (1997). Engel and Hakkio (1996) find that EMS exchange rates have higher volatility dur-