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A CONSISTENT NONPARAMETRIC TEST FOR CAUSALITY INQUANTILE

Published online by Cambridge University Press:  19 January 2012

Kiho Jeong ,
Wolfgang K. Härdle  and
Song Song
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Abstract

This paper proposes a nonparametric test of Granger causality in quantile.Zheng (1998, Econometric Theory 14, 123–138) studied the idea to reduce the problem oftesting a quantile restriction to a problem of testing a particular type ofmean restriction in independent data. We extend Zheng’s approach to the caseof dependent data, particularly to the test of Granger causality inquantile. Combining the results of Zheng (1998) and Fan and Li (1999, Journal of Nonparametric Statistics 10,245–271), we establish the asymptotic normal distribution of the teststatistic under a β-mixing process. The test is consistentagainst all fixed alternatives and detects local alternatives approachingthe null at proper rates. Simulations are carried out to illustrate thebehavior of the test under the null and also the power of the test underplausible alternatives. An economic application considers the causalrelations between the crude oil price, the USD/GBP exchange rate, and thegold price in the gold market.

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Type
Research Article
Information
Econometric Theory , Volume 28 , Issue 4 , August 2012 , pp. 861 - 887
Copyright
Copyright © Cambridge University Press 2012

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Footnotes

The research was conducted while Jeong was visiting C.A.S.E.—Center for Applied Statistics and Economics—Humboldt-Universität zu Berlin in the summers of 2005 and 2007. Jeong is grateful for their hospitality during the visits. Jeong’s work was supported by a Korean Research Foundation grant funded by the Korean government (MOEHRD) (KRF-2006-B00002), and Härdle and Song’s work was supported by the Deutsche Forschungsgemeinschaft through the SFB 649 “Economic Risk.” We thank the editor, two anonymous referees, and Holger Dette for concrete suggestions on improving the manuscript and restructuring the paper. Their valuable comments and suggestions are gratefully acknowledged.

References

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