Spurious logarithms and the KPSS statistic

This paper analyzes the asymptotic behavior of two types of so-called KPSS tests when a logarithm transformation has been applied spuriously to data that are themselves an integrated time series. Although a different limit distribution is obtained, the asymptotic convergence behavior of the KPSS statistic is reminiscent of that of integrated time series, and it is shown that the KPSS test cannot distinguish consistently between an integrated time series and the logarithm of an integrated time series.