The performance of unit root tests under level-dependent heteroskedasticity

Several financial variables exhibit level-dependent conditional heteroskedasticity. This may cause severe distortions in conventional unit root tests. Given the absence of theoretical results, we conduct Monte Carlo investigation to assess the performance of the standard Dickey-Fuller tests, a nonparametric alternative, and a heteroskedastic-robust extension of the Dickey-Fuller t-test. While these procedures have approximately correct size, we find strong distortions in the power of the standard Dickey-Fuller tests.