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Measuring nonlinear Granger causality in mean.

Song, X. and Taamouti, A. (2018) 'Measuring nonlinear Granger causality in mean.', Journal of business and economics statistics., 36 (2). pp. 321-333.


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.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Publisher statement:This is an Accepted Manuscript of an article published by Taylor & Francis Group in Journal of business and economics statistics on 28/04/2016, available online at:
Date accepted:01 February 2016
Date deposited:04 February 2016
Date of first online publication:28 April 2017
Date first made open access:22 March 2017

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