Vector Autoregressive Models With Measurement Errors for Testing Ganger Causality

摘要

This paper develops a method for estimating parameters of a vectorautoregression (VAR) observed in white noise. The estimation method assumes thenoise variance matrix is known and does not require any iterative process. Thisstudy provides consistent estimators and shows the asymptotic distribution ofthe parameters required for conducting tests of Granger causality. Methods inthe existing statistical literature cannot be used for testing Grangercausality, since under the null hypothesis the model becomes unidentifiable.Measurement error effects on parameter estimates were evaluated by usingcomputational simulations. The results show that the proposed approach producesempirical false positive rates close to the adopted nominal level (even forsmall samples) and has a good performance around the null hypothesis. Theapplicability and usefulness of the proposed approach are illustrated using afunctional magnetic resonance imaging dataset.