We propose methods for testing hypothesis of non-causality at various horizons, as defined in Dufour and Renault (1998, Econometrica). We study in detail the case of VAR models and we propose linear methods based on running vector autoregressions at different horizons. While the hypotheses...

We study two linear estimators for stationary invertible VARMA models in echelon form to achieve identification (model parameter unicity) with known Kronecker indices. Such linear estimators are much simpler to compute than Gaussian maximum-likelihood estimators often proposed for such models,...