Bootstrap double frequency dickey fuller test for unit roots

In this paper we present some advances over the Double Frequency Dickey Fuller test for unit root, recently proposed in literature to capture those situations where the time series might be affected by potential unknown structural breaks, asymmetrically located. The Double Frequency Dickey Fuller is based on the idea the Fourier approach allows capturing the behavior of a deterministic function form even if it is not periodic, working better than dummy variables, independent of the breaks are instantaneous or smooth and avoiding the problem of selecting the dates and the form of the breaks. For the Double Frequency Dickey Fuller test, it has been developed the asymptotic theory and, via simulations, its finite sample properties have been shown with respect to a variety of processes. To the best of our knowledge, however, no results have yet been presented to combine this test with using bootstrap methods, in order to possibly improve the finite sample performance. To address this issue, we propose a bootstrap test based on the sieve bootstrap for unit root and intend to conduct an extensive Monte Carlo experiment to evaluate its finite sample performance.