Powerful Unit Root Tests Free of Nuisance Parameters

Abstract

We propose a variance ratio‐type unit root test where the nuisance parameter cancels asymptotically under both the null of a unit root and a local‐to‐unity alternative. Critical values and asymptotic power curves can be computed using standard numerical techniques. Our test exhibits higher power compared with tests that share the virtue of being free of tuning parameters. In fact, the local asymptotic power curves of our procedure get close to the power functions of the point optimal test, where the latter suffers from the drawback of having to correct for a nuisance parameter consistently.

A residual‐based nonparametric variance ratio no‐cointegration test

“…Second, Fisher‐type or union‐of‐rejections decision rules (see, e.g., Bayer and Hanck, 2013) combining the variance ratio test with the ADF test could make no‐cointegration testing more robust against finite sample effects. Finally, the variance ratio approach to no‐cointegration testing might be improved further by extending the unit root tests proposed in Cai and Shintani (2006), Nielsen (2009), or Hosseinkouchack and Hassler (2016) to the regression setting.…”