Estimating fractional unit root distribution with fully modified principle

Abstract

We employ the fully-modified method in the estimation of the fractional unit root distribution. Under very mild restrictions on the kernel functions, we prove that the estimator proposed in this paper can accelerate the convergence rate of the coefficient estimator when the true data generating process is an $I(1+d)$ with $din (-0.5,0.5)$. Our results point to the potential of using the fully-modified principle to construct a powerful unit root test against long memory alternatives.