Nonparametric Test for Causality with Long-range Dependence
Econometrica · 2000 · Volume 68 · Issue 6
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 rateT−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-Tconsistent 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-Tconsistent nor asymptotically normal as is the case with short-range dependent data.
Keywords
Causality, long-range dependence, spectral analysis, distributed lag model, consistent test.
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