It is well known that in a vector autoregressive (VAR) model Granger non-causality is characterized by a set of restrictions on the VAR coefficients. This characterization has been derived under the assumption of non-singularity of the covariance matrix of the innovations. This note shows that...

The contribution of this paper is to investigate a particular form of lack of invariance of causality statements to changes in the conditioning information sets. Consider a discrete-time three-dimensional stochastic process z = (x, y1, y2)0. We want to study causality relationships between the...

This paper investigates, in a particular parametric framework, the geometric meaning of joint unpredictability for a bivariate discrete process. In particular, the paper provides a characterization of the joint unpredictability in terms of distance between information sets in an Hilbert space.

It is well known that in a vector autoregressive (VAR) model Granger non-causality is characterized by a set of restrictions on the VAR coefficients. This characterization has been derived under the assumption of non-singularity of the covariance matrix of the innovations. This note shows that...

This note concerns with the marginal models associated with a given vector autoregressive model. In particular, it is shown that a reduction in the orders of the univariate ARMA marginal models can be determined by the presence of variables integrated with different orders. The concepts and...