A family of nonparametric unit root tests for processes driven by infinite variance innovations

Abstract This paper presents extensions to the family of nonparametric fractional variance ratio (FVR) unit root tests Nielsen (2009. “A Powerful Test Autoregressive Unit Root Hypothesis Based on a Tuning Parameter Free Statistic.” Econometric Theory 25 : 1515–44) under heavy tailed (infinite variance) innovations. In this regard, we first develop asymptotic theory for these FVR setup. We show that limiting distributions are free serial correlation nuisance parameters, but depend tail index infinite process. Then, compare finite sample size and power performance our with well-known parametric ADF test impact shocks. Simulations demonstrate innovations, have desirable properties.