On the finite sample size and power of the generalized KPSS test in the presence of level breaks

Abstract

The KPSS stationarity test is oversized when it is applied to a series containing a strong autoregressive process. Hobijn et al. (2004) demonstrated that the test appears to be better-sized when an automatic-data dependent bandwidth selection procedure is used to estimate the long-run variance of the series. This article examines the impact of level breaks under the null on the finite sample size and power of their generalized KPSS test. It demonstrates that empirical sizes depend critically on the location and the magnitude of the break and that the generalized test is not as robust to variance estimation as was previously thought. The results are shown to be similar to those based on the traditional approach to calculating the KPSS test.

Notes

¹Leybourne and McCabe (1993) extended the KPSS test to examine cointegration; Sephton (1995) provided response surface estimates of critical values; Lee (1996) examines power and size for various autogregressive processes under several different approaches to estimating the variance; Lee and Schmidt (1996) show the test can be used to distinguish between short-memory and long-memory processes while Lee and Ambler (1997) demonstrate it cannot distinguish between short-memory and non-stationary long-memory; Lee et al.. (1997) show size distortion arising from ignoring breaks; Busetti and Harvey (2001, 2003) and Harvey and Mills (2001) derive a test allowing for breaks; Caner and Kilian (2001) demonstrate size distortions in short samples; Lee and Strazicich (2001) provide a test allowing for a break; Carrion-i-Silvestre (2003) shows greater divergence in the test statistic if the wrong breakpoint is chosen relative to failing to allow for a break; Presno and Lopez (2003) provide response surface estimates of critical values allowing for breaks; Darne (2004) shows the test is robust to outliers; and Harvey and Mills (2004) provide tests with endogenously determined structural change.

²See the Monte Carlo evidence presented by Hobijn et al. (2004, pp. 494–5) in particular.