A linear theory for noncausality. (English) Zbl 0601.62137

Florens, J.-P.; Mouchart, M.

Econometrica 53, 157-175 (1985).

The authors analyze different definitions of noncausality (according to Granger, Sims, Pierce and Haugh) in terms of orthogonality in the Hilbert space of square integrable variables. The main purpose of the paper is to give precise statements related to the equivalence among several definitions of noncausality. Furthermore, the authors obtain equivalent p-steps backward Granger’s type conditions and p-step forward Sim’s type conditions. These results allow the systematic treatment of finite horizon noncausality which is crucial for testing purposes.
Proofs of the theorems are given in the appendix, and it should be mentioned that none of the proofs requires stationarity assumptions.

Reviewer: H.S.Buscher

MSC:

62P20

Applications of statistics to economics

Keywords:

Granger-causality; Sims-causality; rational expectations; different definitions of noncausality; orthogonality; Hilbert space of square integrable variables; equivalence; finite horizon noncausality