Granger causality between vectors of time series: A puzzling property

Umberto Triacca

Statistics & Probability Letters, 2018, vol. 142, issue C, 39-43

Abstract: Let us consider a discrete-time n-dimensional stochastic process z, with components x=(x1,…,xm1)′ and y=(y1,…,ym2)′, m1+m2=n. We want to study causality relationships between the variables in x andy. Suppose that we find that y Granger causes x. Then we would expect to be able to pick out at least one of these variables, say yj, having a causal impact on x. It turns out that, when we consider the conditioning information set defined by the past observations of x and all the yi, i≠j, it may be that yj has no causal impact on x, irrespective of the particular j=1,2,…,m2 that we tried to pick out. This is a puzzling property. The paper provides a condition under which this property cannot hold.

Keywords: Granger causality; Hilbert spaces; Time series (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1016/j.spl.2018.06.009

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