Regulated Fractional Variance Ratio Unit Root Tests

This article addresses unit root testing on regulated series through the variance ratio (VR) statistic of Nielsen (2009). The asymptotic distribution of the regulated VR statistic is developed with and without OLS detrending. Results of Cavaliere and Xu (2011) are extended by also developing the asymptotic distribution of regulated series with a linear trend. Asymptotic local power is analyzed for various choices of the fractional integration parameter d. It is shown that power performance depends crucially on the length of the regulating interval. When the interval is sufficiently wide the results in Nielsen (2009) are recovered