(2003) is compared with the new test. The results suggest that the new test is generally superior in terms of power. An application to a real effective exchange rate underlines its usefulness.

Keywords: break in pesistence, long memory, CUSUM of squares based test.

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In this paper we analyze the convergence of interest rates in the European Monetary System (EMS) in a framework of changing persistence. This allows us to estimate the exact date of full convergence from the data. A change in persistence means that a time series switches from stationarity to non-stationarity, or vice versa. It is often argued that due to the specific historical situation in the EMS the interest rate differential was non-stationary before the full convergence of interest rates was achieved and stationary afterwards. Our empirical results suggest that the convergence date has been very different for Belgium, France, the Netherlands and Italy and are in line with the conclusions one would draw from a narrative approach. We compare three different estimators for the convergence date and find that the results are quite robust. Our results therefore stress the importance of credibility for monetary policy.

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This article extends the analysis of local power of unit root tests in a nonlinear direction by considering local nonlinear alternatives and tests built specifically against stationary nonlinear models. In particular, we focus on the popular test proposed by Kapetanios et al. (2003, Journal of Econometrics 112, 359-379) in comparison to the linear Dickey-Fuller test. To this end, we consider different adjustment schemes for deterministic terms. We provide asymptotic results which imply that the error variance has a severe impact on the behaviour of the tests in the nonlinear case; the reason for such behaviour is the interplay of non-stationarity and nonlinearity. In particular, we show that nonlinearity of the data generating process can be asymptotically negligible when the error variance is moderate or large (compared to the 'amount of nonlinearity'), rendering the linear test more powerful than the nonlinear one. Should however the error variance be small, the nonlinear test has better power against local alternatives. We illustrate this in an asymptotic framework of what we call persistent nonlinearity. The theoretical findings of this article explain previous results in the literature obtained by simulation. Furthermore, our own simulation results suggest that the user-specified adjustment scheme for deterministic components (e.g. OLS, GLS, or recursive adjustment) has a much higher impact on the power of unit root tests than accounting for nonlinearity, at least under local (linear or nonlinear) alternatives.ASSUMPTION 2. Let e t be an iid sequence such that E(e t ) ¼ 0, Varðe t Þ ¼ r 2 , and 9d > 0 with E e t j j 4þd < C < 1:LOCAL POWER OF NONLINEAR UNIT ROOT TESTS

This research points to the serious problem of potentially misspecified alternative hypotheses when testing for unit roots in real exchange rates. We apply a popular unit root test against nonlinear ESTAR and develop a Markov Switching unit root test. The empirical power of these tests against correctly and misspecified non-linear alternatives is analyzed by means of a Monte Carlo study. The chosen parametrization is obtained by real-life exchange rates. The test against ESTAR has low power against all alternatives whereas the proposed unit root test against a Markov Switching autoregressive model performs clearly better. An empirical application of these tests suggests that real exchange rates may indeed be explained by Markov-Switching dynamics.