This paper investigates the problem of testing for linear Granger causality in mean when the number of parameters is high with the possible presence of nonlinear dynamics. Dependent innovations are taken into account by considering tests which asymptotic distributions is a weighted sum of chi-squares and tests with modified weight matrices. Wald, Lagrange Multiplier (LM) and Likelihood Ratio (LR) tests for linear causality in mean are studied. It is found that the LM tests based on restricted estimators significantly improve the analysis of linear Granger causality in mean relations when the dimension is high or when the autoregressive order is large. We also see that the tests based on a modified asymptotic distribution have a better control of the error of first kind when compared to the tests with modified statistic in finite samples. An application to international finance data is proposed to illustrate the robustness to the presence of nonlinearities of the studied tests.
"Testing linear causality in mean when the number of estimated parameters is high." Electron. J. Statist. 5 507 - 533, 2011. https://doi.org/10.1214/11-EJS617