Modification of the point optimal unit root test

Abstract

A modification of the existing point optimal unit root test is proposed. The new test has very good finite sample power and is easily correctable via semi-parametric methods. Critical values are provided along with power simulation and empirical examples.

Notes

¹ Other kernels (set of weights) are also useful in practice.

² Alternative assumptions (not examined in this article) include: u ₁ = ∊₁ random with E(∊₁) = 0 and finite variance and the Berenblut and Webb (1973) assumption u ₁ = ∊₁ ∼ N(0, σ²).

³ Certain kernels are better suited to more volatile time series. In practice, test decision depends on the choice of long-run variance estimator employed, which is in effect depends on kernel choice. It may be useful to use various such long-run variance estimators (kernels) and resulting unit root tests before decision.