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Econometrics Paper
Nonparametric Test for Causality with Long-Range Dependence - (Now published in 'Econometrica', 68, (2000) pp.1465-1490.
Javier Hidalgo April 2000
Paper No' EM/2000/387:
Full Paper (pdf)

Tags: causality; long-range dependence; spectral analysis; distributed lag model; consistent test

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-½. 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 is 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.