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...

In this paper we propose a test for a set of linear restrictions in a Vector Autoregressive Moving Average (VARMA) model. This test is based on the autoregressive metric, a notion of distance between two univariate ARMA models, M0 and M1, introduced by Piccolo in 1990. In particular, we show...

A distance between pairs of sets of autoregressive moving average (ARMA) processes is proposed. Its main properties are discussed. The paper also shows how the proposed distance finds application in time series analysis. In particular it can be used to evaluate the distance between portfolios of...

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...

This paper characterizes the impact of serial dependence on the non-asymptotic estimation error bound of penalized regressions (PRs). Focusing on the direct relationship between the degree of cross-correlation of covariates and the estimation error bound of PRs, we show that orthogonal or weakly...

We address the problem of selecting the common factors that are relevant for forecasting macroeconomic variables. In economic forecasting using diffusion indexes the factors are ordered, according to their importance, in terms of relative variability, and are the same for each variable to...

We address the problem of selecting the common factors that are relevant for forecasting macroeconomic variables. In economic forecasting using diffusion indexes the factors are ordered, according to their importance, in terms of relative variability, and are the same for each variable to...

We address the problem of selecting the common factors that are relevant for forecasting macroeconomic variables. In economic forecasting using diffusion indexes the factors are ordered, according to their importance, in terms of relative variability, and are the same for each variable to...