In this note the relationship between alternative concepts of noncausality is analyzed using the tool of conditional independence among a-fields. (For the reader who is unfamiliar with this technique, the Appendix sketches the proofs and the basic technical apparatus, along with some basic motivations.) Furthermore, the relationship between the concepts of noncausality and transitivity is made explicit in order to facilitate, in econometric modelling, the use of results already obtained in sequential analysis.
Florens, J. P., & Mouchart, M. (1982). A Note on Noncausality. Econometrica, 50(3), 583-591. https://hdl.handle.net/2078.5/77459 (Original work published 1982)