a1 Kyungpook National University
a2 Humboldt-Universität zu Berlin
a3 Humboldt-Universität zu Berlin and University of California, Berkeley
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 of testing a quantile restriction to a problem of testing a particular type of mean restriction in independent data. We extend Zheng’s approach to the case of dependent data, particularly to the test of Granger causality in quantile. 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 test statistic under a β-mixing process. The test is consistent against all fixed alternatives and detects local alternatives approaching the null at proper rates. Simulations are carried out to illustrate the behavior of the test under the null and also the power of the test under plausible alternatives. An economic application considers the causal relations between the crude oil price, the USD/GBP exchange rate, and the gold price in the gold market.
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.