A nonparametric unit root test under nonstationary volatility

•A nonparametric unit root test robust to nonstationary volatility is proposed.•The proposed test statistic does not require a correction of serial correlation.•The proposed test is correctly sized and has desirable power.•In finite sample properties, our test outperforms other tests in the literature.

We develop a new nonparametric unit root testing method that is robust to permanent shifts in innovation variance. Unlike other methods in the literature, our test does not require a parametric specification or lag/bandwidth selection to adjust for serial correlation.