A Consistent Nonparametric Test for Causality in Quantile

A Consistent Nonparametric Test for Causality in Quantile

This paper proposes a nonparametric test of Granger causality in quantile. Zheng(1998) has proposed an 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), we establish the asymptotic normal distribution of the test statistic under beta mixing process. The test is consistent against all fixed alternatives and detects local alternatives approaching to the null at proper rates.