p.1465

Nonparametric Test for Causality with Long-range Dependence

Javier Hidalgo

Abstract

This paper introduces a nonparametric Granger-causality test for covariance stationary linear processes under, possibly, the presence of long-range dependence. We show that the test is consistent and has power against contiguous alternatives converging to the parametric rate T^−1/2. Since the test is based on estimates of the parameters of the representation of a VAR model as a, possibly, two-sided infinite distributed lag model, we first show that a modification of Hannan’s (1963, 1967) estimator is root- T consistent and asymptotically normal for the coefficients of such a representation. When the data are long-range dependent, this method of estimation becomes more attractive than least squares, since the latter can be neither root- T consistent nor asymptotically normal as is the case with short-range dependent data.