Noncausality in Continuous Time.

Different concepts of noncausality for continuous time processes, using conditional independence and decomposition of semimartingales, are defined. 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 semimartingales for which, in general, the weak instantaneous noncausality does not imply the strong global noncausality. The paper then characterizes these different concepts in the case of counting processes and Markov processes. Copyright 1996 by The Econometric Society.