  This paper derives asymptotic theory for Breitung's (2002, Journal of
Econometrics 108, 343-363) nonparameteric variance ratio unit root test when
applied to regression residuals. The test requires neither the specification of
the correlation structure in the data nor the choice of tuning parameters.
Compared with popular residuals-based no-cointegration tests, the variance
ratio test is less prone to size distortions but has smaller local asymptotic
power. However, this paper shows that local asymptotic power properties do not
serve as a useful indicator for the power of residuals-based no-cointegration
tests in finite samples. In terms of size-corrected power, the variance ratio
test performs relatively well and, in particular, does not suffer from power
reversal problems detected for, e.g., the frequently used augmented
Dickey-Fuller type no-cointegration test. An application to daily prices of
cryptocurrencies illustrates the usefulness of the variance ratio test in
practice.
