Noncausality in Continuous Time

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 nonc...

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Bibliographic Details
Published in:Econometrica 1996-09, Vol.64 (5), p.1195-1212
Main Authors: Florens, Jean-Pierre, Fougere, Denis
Format: Article
Language:English
Subjects:
Causality
Econometric models
Econometrics
Economic models
Economic theory
Exact sciences and technology
Markov analysis
Markov processes
Markovian processes
Martingale
Martingales
Mathematical functions
Mathematical vectors
Mathematics
Partial differential equations
Probabilities
Probability and statistics
Probability theory and stochastic processes
Random variables
Sciences and techniques of general use
Stochastic processes
Stopping distances
Studies
Time series
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Summary: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.
ISSN:0012-9682
1468-0262
DOI:10.2307/2171962