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Noncausality in Continuous Time Models

Published online by Cambridge University Press:  11 February 2009

F. Comte  and
E. Renault
F. Comte
Affiliation:
Université Paris I
E. Renault
Affiliation:
Université de Toulouse and Institut Universitaire de France
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Abstract

In this paper, we study new definitions of noncausality, set in a continuous time framework, illustrated by the intuitive example of stochastic volatility models. Then, we define CIMA processes (i.e., processes admitting a continuous time invertible moving average representation), for which canonical representations and sufficient conditions of invertibility are given. We can provide for those CIMA processes parametric characterizations of noncausality relations as well as properties of interest for structural interpretations. In particular, we examine the example of processes solutions of stochastic differential equations, for which we study the links between continuous and discrete time definitions, find conditions to solve the possible problem of aliasing, and set the question of testing continuous time noncausality on a discrete sample of observations. Finally, we illustrate a possible generalization of definitions and characterizations that can be applied to continuous time fractional ARMA processes.

Type
Research Article
Information
Econometric Theory , Volume 12 , Issue 2 , June 1996 , pp. 215 - 256
Copyright
Copyright © Cambridge University Press 1996

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