The power of unit root tests against nonlinear local alternatives

This article extends the analysis of local power of unit root tests in a nonlinear direction by considering local nonlinear alternatives and nonlinear tests. The foci are (i) on nonlinear smooth transition models and the related nonlinear unit root test proposed by Kapetanios et al. (2003, Journal of Econometrics 112, 359-379), and (ii) on the comparison of different adjustment schemes for deterministic terms for the considered nonlinear test. We provide asymptotic results which imply that the error variance has a severe impact on the behavior of the tests in the nonlinear case; the reason for such behavior is the interplay of nonstationarity and nonlinearity. Moreover, we show that the nonlinearity of the data generating process can be asymptotically negligible when the error variance is moderate or large (compared to the “amount of nonlinearity” of the data generating process), rendering the linear Dickey-Fuller test more powerful than the nonlinear test. Should however the error variance be small, the nonlinear test has better power against local alternatives. The theoretical findings of this paper 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) is far more important for the power of unit root tests than accounting for nonlinearity, at least when the alternative is close to the null.

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