Vector autoregressive models with measurement errors for testing Granger causality

This paper develops a method for estimating the parameters of a vector autoregression (VAR) observed in white noise. The estimation method assumes that the noise variance matrix is known and does not require any iterative process. This study provides consistent estimators and the asymptotic distribution of the parameters required for conducting tests of Granger causality. Methods in the existing statistical literature cannot be used for testing Granger causality, since under the null hypothesis the model becomes unidentifiable. Measurement error effects on parameter estimates were evaluated by using computational simulations. The results suggest that the proposed approach produces empirical false positive rates close to the adopted nominal level (even for small samples) and has a satisfactory performance around the null hypothesis. The applicability and usefulness of the proposed approach are illustrated using a functional magnetic resonance imaging dataset.