A combined nonparametric test for seasonal unit roots

Nonparametric unit-root tests are a useful addendum to the tool-box of time-series analysis. They tend to trade off power for enhanced robustness features. We consider combinations of the RURS (seasonal range unit roots) test statistic and a variant of the level-crossings count. This combination exploits two main characteristics of seasonal unit-root models, the range expansion typical of integrated processes and the low frequency of changes among main seasonal shapes. The combination succeeds in achieving power gains over the component tests. Simulations explore the finite-sample behavior relative to traditional parametric tests.