Econometrica: Nov 2000, Volume 68, Issue 6

Nonparametric Test for Causality with Long‐range Dependence
p. 1465-1490

Javier Hidalgo

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 . 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‐ 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‐ consistent nor asymptotically normal as is the case with short‐range dependent data.

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