Scandinavian Working Papers in Economics

Working Papers,
Lund University, Department of Economics

No 2006:23: Finite-Sample Stability of the KPSS Test

Kristian Jönsson ()
Additional contact information
Kristian Jönsson: Sveriges Riksbank, Postal: Macroprudential Division, Financial Stability Department, Sveriges Riksbank, SE-103 37 Stockholm, Sweden,

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

JEL-codes: C12; C13; C14; C15; C22; E21

32 pages, December 14, 2006

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