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.