Introduction

A number of studies consider testing for unit roots in univariate time series which have a level shift. Examples are Perron (1989, 1990), Perron and Vogelsang (1992), Banerjee, Lumsdaine, and Stock (1992), Zivot and Andrews (1992), Amsler and Lee (1995), Leybourne, Newbold, and Vougas (1998), Montanes and Reyes (1998), and Saikkonen and Lütkepohl (1999). These tests are important because the trending properties of a set of time series determine to some extent which model and statistical procedures are suitable for analyzing their relationship. In the aforementioned studies different models and assumptions for the structural shift are considered. In some of the studies the timing of the break point is assumed to be known, whereas in others a shift in an unknown period is considered. There seems to be general consensus, however, that if the break point is known, this is useful information which should be taken into account in the subsequent analysis and in particular in testing for unit roots. Therefore we will focus on the latter case in the following. In practice, a known break point is quite common. For instance, many German macroeconomic time series are known to have a shift in 1990 where the German reunification took place.

For the case of a known break point we will propose a framework which generalizes previously considered models. In this framework the shift is modeled as part of the intercept term of the stationary part of the data generation process (DGP) which is clearly separated from the unit root part.