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Measuring Nonlinear Granger Causality in Mean

Song, X.; Taamouti, A.

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Authors

X. Song



Abstract

We propose model-free measures for Granger causality in mean between random variables. Unlike the existing measures, ours are able to detect and quantify nonlinear causal effects. The new measures are based on nonparametric regressions and defined as logarithmic functions of restricted and unrestricted mean square forecast errors. They are easily and consistently estimated by replacing the unknown mean square forecast errors by their nonparametric kernel estimates. We derive the asymptotic normality of nonparametric estimator of causality measures, which we use to build tests for their statistical significance. We establish the validity of smoothed local bootstrap that one can use in finite sample settings to perform statistical tests. Monte Carlo simulations reveal that the proposed test has good finite sample size and power properties for a variety of data-generating processes and different sample sizes. Finally, the empirical importance of measuring nonlinear causality in mean is also illustrated. We quantify the degree of nonlinear predictability of equity risk premium using variance risk premium. Our empirical results show that the variance risk premium is a very good predictor of risk premium at horizons less than six months. We also find that there is a high degree of predictability at horizon one-month which can be attributed to a nonlinear causal effect.

Citation

Song, X., & Taamouti, A. (2018). Measuring Nonlinear Granger Causality in Mean. Journal of Business & Economic Statistics, 36(2), 321-333. https://doi.org/10.1080/07350015.2016.1166118

Journal Article Type Article
Acceptance Date Feb 1, 2016
Online Publication Date Apr 28, 2017
Publication Date Jan 1, 2018
Deposit Date Feb 3, 2016
Publicly Available Date Mar 22, 2017
Journal Journal of Business and Economic Statistics
Print ISSN 0735-0015
Electronic ISSN 1537-2707
Publisher Taylor and Francis Group
Peer Reviewed Peer Reviewed
Volume 36
Issue 2
Pages 321-333
DOI https://doi.org/10.1080/07350015.2016.1166118
Public URL https://durham-repository.worktribe.com/output/1393270

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