In this paper an expression is obtained for the determinant of a particular patterned matrix. The result is then used to derive the partial autocorrelation function of a first order non-invertible moving average process.

In time series analysis, a vector Y is often called causal for another vector X if the former helps to improve the k-step-ahead forecast of the latter. If this holds for k= 1, vector Y is commonly called Granger-causal for X. It has been shown in several studies that the finding of causality...

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, <em>M₀</em> and <em>M₁</em>, introduced by Piccolo in 1990. In particular, we show...

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...