Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Sep, 1996, Volume 64, Issue 5

Noncausality in Continuous Time<1195:NICT>2.0.CO;2-F
p. 1195-1212

Denis Fougere, Jean-Pierre Florens

In this paper, we define different concepts of noncausality for continuous-time processes, using conditional independence and decomposition of semi-martingales. These definitions extend the ones already given in the case of discrete-time processes. As in the discrete-time setup, continuous-time noncausality is a property concerned with the prediction horizon (global versus instantaneous noncausality) and the nature of the prediction (strong versus weak noncausality). Relations between the resulting continuous-time noncausality concepts are then studied for the class of decomposable semi-martingales, for which, in general, the weak instantaneous noncausality does not imply the strong global noncausality. The paper than characterizes these different concepts of noncausality in the cases of counting processes and Markov processes.

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