Working Papers, Department of Economics, Lund University
No 2006:23:
Finite-Sample Stability of the KPSS Test
Kristian Jönsson ()
Abstract: In the current paper, the finite-sample stability of
various implementations of the KPSS test is studied. The implementations
considered differ in how the so-called long-run variance is estimated under
the null hypothesis. More specifically, the effects that the choice of
kernel, the value of the bandwidth parameter and the application of a
prewhitening filter have on the KPSS test are investigated. It is found
that the finite-sample distribution KPSS test statistic can be very
unstable when the Quadratic Spectral kernel is used and/or a prewhitening
filter is applied. The instability manifests itself through making the
small-sample distribution of the test statistic sensitive to the specific
process that generates the data under the null hypothesis. This in turn
implies that the size of the test can be hard to control. For the cases
investigated in the current paper, it turns out that using the Bartlett
kernel in the long-run variance estimation renders the most stable test. By
supplying an empirical application, we illustrate the adverse effects that
can occur when care is not taken in choosing what test implementation to
employ when testing for stationarity in small-sample situations.
Keywords: Stationarity; Unit root; KPSS test; Size distortion; Long-run variance; Monte Carlo simulation; Private consumption; Permanent Income Hypothesis; (follow links to similar papers)
JEL-Codes: C12; C13; C14; C15; C22; E21; (follow links to similar papers)
32 pages, December 14, 2006
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