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A NONPARAMETRIC TEST FOR INSTANTANEOUS CAUSALITY WITH TIME-VARYING VARIANCES

Published online by Cambridge University Press:  21 February 2025

Jilin Wu,
Ruike Wu and
Zhijie Xiao
Jilin Wu*
Affiliation:
Xiamen University
Ruike Wu
Affiliation:
Shanghai University of Finance and Economics
Zhijie Xiao
Affiliation:
Boston College
*
Address correspondence to Jilin Wu, Department of Finance, School of Economics, Gregory and Paula Chow Institute for studies in Economics, and MOE Key Laboratory of Econometrics, Xiamen University, Xiamen, China, e-mail: rainforest1061@126.com.
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Abstract

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This paper proposes a consistent nonparametric test with good sampling properties to detect instantaneous causality between vector autoregressive (VAR) variables with time-varying variances. The new test takes the form of the U-statistic, and has a limiting standard normal distribution under the null. We further show that the test is consistent against any fixed alternatives, and has nontrivial asymptotic power against a class of local alternatives with a rate slower than $T^{-1/2}$. We also propose a wild bootstrap procedure to better approximate the finite sample null distribution of the test statistic. Monte Carlo experiments are conducted to highlight the merits of the proposed test relative to other popular tests in finite samples. Finally, we apply the new test to investigate the instantaneous causality relationship between money supply and inflation rates in the USA.

Information

Type
ARTICLES
Information
Econometric Theory , Volume 42 , Issue 2 , April 2026, pp. 414 - 442
Copyright
© The Author(s), 2025. Published by Cambridge University Press

Footnotes

Jilin Wu acknowledges the supports from the National Natural Science Foundation of China (Grant No. 72371213) and from the NSFC Basic Science Center Project for Econometric Modeling and Economic Policy Studies (Grant No. 71988101). We are most grateful to the Editor, Peter Phillips, for carefully going through an earlier version of the paper and providing many pertinent comments and constructive suggestions that markedly improved the paper. We also would like to thank the Co-Editor (Xu Cheng), and three referees for their constructive comments and suggestions. The authors contributed equally to this paper and are credited in alphabetical order.

References

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