Nonlinear Granger Causal Paths, Dependence Measures and Canonical Correlations

A popular F test of Granger-causality relies on normally distributed errors of ordinary least squares (OLS) linear regressions. There is a long-standing need for a user-friendly algorithm replacing the OLS by kernel regressions, and the F test by a bootstrap. This paper introduces a version (1.1.6) of the R package 'generalCorr' which offers (bootGcRsq) to satisfy the need. Granger causality requires the 'cause' to occur at a time before the 'effect' occurs, ruling out instantaneous causality. The R command (causeSummary) for assessing instantaneous causality possibly in cross-sectional data is now enhanced by (causeSummBlk). The command (gmcmtx0) for the non-symmetric matrix of generalized correlation coefficients R* is enhanced by (gmcmtxBlk). The asymmetric R* leads to two new concepts, (i) measures of dependence implemented by the command (depMeas), and (ii) generalized canonical correlations which explicitly incorporate pairwise non-linear dependence between linear combinations of variables. The latter needs a new Lagrangian maximization implemented by the command (canonRho). We illustrate its application using joint production of wool and mutton by capital and labor