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A Linear Theory for Noncausality

J.-P. Florens
M. Mouchart

Abstract

Different definitions of noncausality (according to Granger, Sims, Pierce and Haugh), are analyzed in terms of orthogonality in the Hilbert space of square integrable variables. Conditions, when necessary, are given for their respective equivalence. Some problems of testability are mentioned. Finally noncausality is also analyzed in terms of "rational expectations," extending previous results of Sims.