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Nonparametric estimation and inference for conditional density based Granger causality measures. (English) Zbl 1293.62082

Summary: We propose a nonparametric estimation and inference for conditional density based Granger causality measures that quantify linear and nonlinear Granger causalities. We first show how to write the causality measures in terms of copula densities. Thereafter, we suggest consistent estimators for these measures based on a consistent nonparametric estimator of copula densities. Furthermore, we establish the asymptotic normality of these nonparametric estimators and discuss the validity of a local smoothed bootstrap that we use in finite sample settings to compute a bootstrap bias-corrected estimator and to perform statistical tests. A Monte Carlo simulation study reveals that the bootstrap bias-corrected estimator behaves well and the corresponding test has quite good finite sample size and power properties for a variety of typical data generating processes and different sample sizes. Finally, two empirical applications are considered to illustrate the practical relevance of nonparametric causality measures.

MSC:

62G05 Nonparametric estimation
62G07 Density estimation
62H05 Characterization and structure theory for multivariate probability distributions; copulas
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62P05 Applications of statistics to actuarial sciences and financial mathematics
91G70 Statistical methods; risk measures
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