Residual-based block bootstrap unit root testing in the presence of trend breaks

In this paper, we build on the 'residual-based block bootstrap unit root testing' (RBB) method, proposed by Paparoditis and Politis (2003). We develop an extension of this method to allow for bootstrap unit root testing in a model defined by an augmented Dickey-Fuller (ADF) equation that contains linear combinations of arbitrary dummies as its deterministic part. The main application of such an extension is that it allows for unit root testing in the presence of arbitrary multiple trend breaks, such as jumps or changes of the slope of a linear trend. The model framework used here is an extension of Perron's 'innovational outlier model', and allows as well for gradual transitions of the expectation of the series when such breaks or outliers occur; this assumption is particularly appealing in the context of analysing economic time series. Our extension of the bootstrap method involves specifying a drift term and adjustments for the expectation of the residuals and the pseudo-differences, which all appropriately take into account the dependency structure. We prove asymptotic validity of the proposed modified bootstrap procedure in the case of a single break in slope. The small sample behaviour of the proposed methodology is studied in a simulation experiment.