A Consistent Nonparametric Test for Causality in Quantile

A Consistent Nonparametric Test for Causality in Quantile

Kiho Jeong

School of Economics and Trade
Kyungpook National University
Daegu 702-701, Korea

Email: [email protected]

Wolfgang Karl Hardle
CASE - Center for Applied Statistics and Economics
Humboldt-Universitat zu Berlin
Wirtschaftswissenschaftliche Fakultat
Spandauer Strasse 1, 10178 Berlin, Germany
Email: [email protected]
13. 9. 2007

Abstact

This paper proposes a nonparametric test of 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. The proposed
test statistic is shown to have a second-order degenerate U-statistic as a
leading term under the null hypothesis. Using the result on the asymptotic
normal distribution for a general second order degenerate U-statistics with
weakly dependent data of Fan and Li (1996), we establish the asymptotic
distribution of the test statistic for causality in quantile under β-mixing
(absolutely regular) process.

Key Words: Granger Causality, Quantile, Nonparametric Test

JEL classification: C14, C52

We thank Jürgen Franke for his Matlab code to compute a nonparametric kernel estimator of
conditional quantile. The research was conducted while Jeong was visiting CASE-Center for
Applied Statistics and Economics, Humboldt-Universitat zu Berlin in summers of 2005 and
2007. Jeong is grateful for their hospitality during the visit. Jeong’s work was supported by
the Korean Research Foundation Grant funded by the Korean Government (MOEHRD)
(KRF-2006-B00002) and Hardle’s work was supported by the Deutsche
Forschungsgemeinschaft through the SFB 649 "Economic Risk".

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