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RESEARCH PRODUCT

A PROOF OF THE POWER OF KIM'S TEST AGAINST STATIONARY PROCESSES WITH STRUCTURAL BREAKS

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Recently, Kim (2000)1 and Busetti and Taylor (2004) have proposed different ratio-based procedures to test the hypothesis of stationarity against the alternative of changing persistence.2 This includes the alternative of a process changing from 1(0) to I(1) and vice versa, although Busetti and Taylor (2004) show that Kim's original test (2000) is inconsistent against fixed I(1) I(0) alternatives. In this note we show that, similarly to other stationarity tests (e.g., Kwiatkowski, Phillips, Schmidt, and Shin [KPSS]), Kim's test (2000) rejects the null of stationarity asymptotically with probability one, whenever the true data generating process is a stationary one around a constant term with a break. This provokes an indeterminacy in identifying the source of the rejection: is it due to a true change of persistence, or is it due to a break in the deterministic components? The next section shows the properties of Kim's test (2000) when the true data generating process is I(0) around a constant term, suddenly shifted by a structural change.