Granger spurious causality test based on the perspective of HAC estimation

The study finds that spurious Granger causality occurs between independent weak stationary processes,and the Wald statistic modified by the traditional H AC method has higher probability of spurious causality than the primitive Wald statistic.At the same time,the paper shows that estimation of the longrun variance is the underlying reason of occurring spurious causality,the Granger causality test statistic constructed based on modified truncation parameter of traditional HAC method has a limiting distribution that does not depend on nuisance parameters.Through setting various weak stationary processes and using Monte-Carlo simulation technology,the paper finds that the new Wald* statistic can greatly decrease the probability of occurring spurious causality,and it is robust to the persistence of data process and sample size,but has some test size distortions.