Detecting multiple level shifts in bounded time series

Abstract

The paper proposes a sequential statistical procedure to test for the presence of level shifts affecting bounded time series, regardless of their order of integration. The paper shows that bounds are relevant for the statistic that assume that the time series are integrated of order one, whereas they do not affect the limiting distribution of the statistic that is defined for time series that are integrated of order zero. The paper proposes a union rejection statistic for bounded processes that does not require information about the order of integration of the stochastic processes. The model specification is general enough to consider the existence of structural breaks that can affect either the level of the time series and/or the bounds that limit its evolution. Monte Carlo simulations indicate that the procedure works well in finite samples. An empirical application that focuses on the Swiss franc against the euro exchange rate evolution illustrates the usefulness of the proposal.