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Reducing the size distortion of the KPSS test. (English) Zbl 1416.62466
Summary: We propose a new stationarity test based on the KPSS test with less size distortion. We extend the boundary rule proposed by D. Sul et al. [“Prewhitening bias in HAC estimation”, Oxf. Bull. Econ. Stat. 67, 517–546 (2005)] to the autoregressive spectral density estimator and parametrically estimate the long-run variance. We also derive the finite sample bias of the numerator of the test statistic up to the \(1/T\) order and propose a correction to the bias term in the numerator. Finite sample simulations show that the correction term effectively reduces the bias in the numerator and that the finite sample size of our test is close to the nominal one as long as the long-run parameter in the model satisfies the boundary condition.

MSC:
62M07 Non-Markovian processes: hypothesis testing
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