Adaptive long memory testing under heteroskedasticity

This paper considers adaptive hypothesis testing for the fractional differencing parameter in a parametric ARFIMA model with unconditional heteroskedasticity of unknown form. A weighted score test based on a nonparametric variance estimator is proposed and shown to be asymptotically equivalent, under the null and local alternatives, to the Neyman-Rao effective score test constructed under Gaussianity and known variance process. The proposed test is therefore asymptotically efficient under Gaussianity. The finite sample properties of the test are investigated in a Monte Carlo experiment and shown to provide potentially large power gains over the usual unweighted long memory test.