Open Access
2011 Testing linear causality in mean when the number of estimated parameters is high
Hamdi Raïssi
Electron. J. Statist. 5: 507-533 (2011). DOI: 10.1214/11-EJS617


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.


Download Citation

Hamdi Raïssi. "Testing linear causality in mean when the number of estimated parameters is high." Electron. J. Statist. 5 507 - 533, 2011.


Published: 2011
First available in Project Euclid: 3 June 2011

zbMATH: 1274.62613
MathSciNet: MR2813553
Digital Object Identifier: 10.1214/11-EJS617

Primary: 62M10
Secondary: 91B84

Keywords: causality in variance , high dimensional processes , large autoregressive order , Linear causality in mean , VAR models , weak errors

Rights: Copyright © 2011 The Institute of Mathematical Statistics and the Bernoulli Society

Back to Top