Both seasonal unit roots and periodic variation can be prevalent in data. In the testing of under variation, validity existing methods, such as HEGY test, remains unknown. The behavior augmented test unaugmented is analyzed. It turns out that asymptotic null distributions statistics single at 1 or − when there are identical to no variation. On other hand, any coexistence 1, , i non-standard dif...

This paper analyzes the mean reversion and unit root properties of general diffusion models and their discrete samples. In particular, we find that the Dickey-Fuller unit root test applied to discrete samples from a diffusion model becomes a test of no mean reversion rather than a unit root, or more generally, nonstationarity in the underlying diffusion. The unit root test has a well defined li...