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.

Following Wold (1954), a causal relationship from a vector y of economic variables towards a vector x should be interpreted through a fictive controlled experiment. At least one factor y(i) component of y should have an impact on x when other factors y(j), j≠i, are kept constant. It is...

A new non-causality test based on the notion of distance between ARMA models is proposed in this paper. The advantage of this test is that it can be used in possible integrated and cointegrated systems, without pre-testing for unit roots and cointegration. The Monte Carlo experiments indicate...

In this note, it is argued that cointegration augments the distance between the differenced series. If two series, x <Subscript> t </Subscript> and y <Subscript> t </Subscript>, are integrated of order one and cointegrated and v <Subscript> t </Subscript> and w <Subscript> t </Subscript> are integrated of order one but not cointegrated then, under certain conditions, the distance...</subscript></subscript></subscript></subscript>

This paper proposes a new approach to estimate the overnight volatility of an individual stock return. Since markets generally do not trade during the overnight period, measures of realized volatility cannot be computed on a “high-frequency” basis. Some studies have resorted to using the...

This paper discusses the joint unpredictability of asset returns on two markets. It provides a necessary condition for joint unpredictability in term of distance between information sets. We conclude that the joint unpredictability requires a condition very strong and so, in this sense, it...

The purpose of this paper is to analyze in bivariate vector autoregression the relationship between feedback in stochastic systems, Granger causality and a measure of dissimilarity between ARMA models. In particular, we consider a bivariate vector autoregressive processes of order p (a bivariate...

If V, A and B are three closed subspaces of we say that V is a splitting subspace for A,B if and only if A and B are conditionally orthogonal given V. If V is a splitting subspace for A,B, we shall say that V splits A,B. Rozanov [Rozanov, Y.A., 1979. Stochastic Markovian Fields. In:...