15.3 Tests for $ I(0)$ against fractional alternatives

A common feature of the first three tests is the use of the heteroskedastic and autocorrelation consistent (HAC) estimator of the variance (Newey and West; 1987) for normalisation. The lag-length $ Q$ is a user-chosen number.

(i)
Lo's robust rescaled range test (Lo; 1991)): lo

(ii)
KPSS test (Kwiatkowski, Phillips, Schmidt, and Shin; 1992): KPSS

(iii)
GKL test (Giraitis, Kokoszka and Leipus; 1998): rvlm
The fourth is a nonparametric test
(iv)
Lobrob Test (Lobato and Robinson; 1998): lobrob
This test is nonparametric in the sense that the test is constructed using the approximation of the spectrum. The bandwidth can be an user-chosen number but Lobato and Robinson (1998) has suggested a plausible m for empirical applications.