Cai and Shintani (2006, Econometric Theory, 22, 347–372) considered the impact of introducing an inconsistent long-run variance estimator when constructing a class of kernel-based ratio tests for testing non-stationarity in the series. They found that the quotient of two estimators with different rates of convergence under the null and the alternative hypotheses may lead to a test having an interesting size and power trade-off. This paper develops modified versions of this test, presents new asymptotic results and tabulates critical values. The finite sample performance is explored through Monte Carlo simulations. The results show that the modifications proposed lead to more powerful unit root tests.
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Ferrer-Pérez, H., Ayuda, M. & Aznar, A. Improving the Performance of a Long-Run Variance Ratio Test for a Unit Root. JER 70, 258–274 (2019). https://doi.org/10.1111/jere.12185
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