Critical values of the augmented fractional Dickey–Fuller test

Abstract

This paper presents response surface estimates of finite sample critical values of the Augmented Fractional Dickey–Fuller test of Dolado et al. (Testing I(1) against I(d) alternatives in the presence of deterministic components. Universidad Carlos III, Madrid, mimeo, 2006). The null hypothesis that a series contains a unit root is tested against the alternative that it is fractionally integrated. It is shown that finite sample critical values depend critically on the lag order used to construct the test statistic as well as the hypothesized value of the fractional differencing parameter under the alternative. Non-linear non-parametric response surfaces provide a novel approach to constructing estimates of finite sample critical values.