NONPARAMETRIC TEST FOR CAUSALITYWITH LONG-RANGE DEPENDENCE*

by

Javier HidalgoLondon School of Economics and Political Science

Contents:Abstract1. Introduction2. Estimation Procedure and its Motivation3. Statistical Framework and Asymptotic Properties

of the Spectral Density Matrix Estimator4. The Asymptotic Dsitribution of the HI Estimator5. A Nonparametric Causality Test6. Implementation of the Test and its Extension to

Multivariate Data7. ConclusionsReferencesMathematical Appendix AMathematical Appendix B

The Suntory CentreSuntory and Toyota International Centresfor Economics and Related DisciplinesLondon School of Economics and PoliticalScience

Discussion Paper Houghton StreetNo. EM/00/387 London WC2A 2AEApril 2000 Tel.: 020 7405 7686

* Previous versions of this article have been circulated under the title Estimation of

distributed lag models with long-range dependence.This article is based on research funded by the Economic and Social ResearchCouncil (ESRC) reference no. R000238212. I thank Andrew Harvey, Peter Robinson,a co-editor, and two referees for helpful comments which led to a much improvedversion of the article. Any remaining errors are, of course, the sole responsibility ofthe author. E-mail: f.j.hidalgo@lse.ac.uk/

Abstract

This paper introduces a nonparametric Granger-causality test for covariancestationary linear processes under, possibly, the presence of long-rangedependence. We show that the test is consistent and has power againstcontiguous alternatives converging to the parametric rate T-½. Since the test isbased on estimates of the parameters of the representation of a VAR modelas a, possibly, two-sided infinite distributed lag model, we first show that amodification of Hannan’s (1963, 1967) estimator is root-T consistent andasymptotically normal for the coefficients of such a representation. When thedata is long-range dependent this method of estimation becomes moreattractive than Least Squares, since the latter can be neither root-T consistentnor asymptotically normal as is the case with short-range dependent data.

Keywords: Causality; long-range dependence; spectral analysis; distributedlag model; consistent test.

JEL Nos.: C12, C13, C32.

© Javier Hidalgo. All rights reserved. Short sections of text, not to exceed twoparagraphs, may be quoted without explicit permission provided that fullcredit, including © notice, is given to the source.

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