NONCAUSALITY IN CONTINUOUS-TIME MODELS

In this paper, we study new definitions of noncausality, set in a cont inuous time framework, illustrated by the intuitive example of stochas tic 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 inv ertibility are given. We can provide for those CIMA processes parametr ic characterizations of noncausality relations as well as properties o f interest for structural interpretations. In particular, we examine t he example of processes solutions of stochastic differential equations , for which we study the links between continuous and discrete time de finitions, find conditions to solve the possible problem of aliasing, and set the question of testing continuous time noncausality on a disc rete sample of observations, Finally, we illustrate a possible general ization of definitions and characterizations that can be applied to co ntinuous time fractional ARMA processes.