{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,29]],"date-time":"2025-12-29T18:45:41Z","timestamp":1767033941967},"reference-count":28,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2009,2,11]],"date-time":"2009-02-11T00:00:00Z","timestamp":1234310400000},"content-version":"unspecified","delay-in-days":5795,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[1993,4]]},"abstract":"<jats:p>In this paper it is shown that a subprocess of a Markov process is markovian if a suitable condition of noncausality is satisfied. Furthermore, a markovian condition is shown to be a natural condition when analyzing the role of the horizon (finite or infinite) in the property of noncausality. We also give further conditions implying that a process is both jointly and marginally markovian only if there is both finite and infinite noncausality and that a process verifies both finite and infinite noncausality only if it is markovian. Counterexamples are also given to illustrate the cases where these further conditions are not satisfied.<\/jats:p>","DOI":"10.1017\/s0266466600007520","type":"journal-article","created":{"date-parts":[[2009,3,10]],"date-time":"2009-03-10T15:47:46Z","timestamp":1236700066000},"page":"241-262","source":"Crossref","is-referenced-by-count":18,"title":["Noncausality and Marginalization of Markov Processes"],"prefix":"10.1017","volume":"9","author":[{"given":"J.P.","family":"Florens","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M.","family":"Mouchart","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J.M.","family":"Rolin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2009,2,11]]},"reference":[{"key":"S0266466600007520_ref018","doi-asserted-by":"publisher","DOI":"10.2307\/1912791"},{"key":"S0266466600007520_ref002","first-page":"223","article-title":"On statistics independent of a sufficient statistic","volume":"20","author":"Basu","year":"1958","journal-title":"Sankhya"},{"key":"S0266466600007520_ref019","doi-asserted-by":"publisher","DOI":"10.1016\/0165-1889(80)90069-X"},{"key":"S0266466600007520_ref004","doi-asserted-by":"publisher","DOI":"10.2307\/1913158"},{"key":"S0266466600007520_ref001","first-page":"377","article-title":"On statistics independent of a complete sufficient statistic","volume":"15","author":"Basu","year":"1955","journal-title":"Sankhya"},{"key":"S0266466600007520_ref005","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177703737"},{"key":"S0266466600007520_ref015","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1982.10477803"},{"key":"S0266466600007520_ref009","volume-title":"Non-causality in continuous time: Application to counting processes","author":"Florens","year":"1991"},{"key":"S0266466600007520_ref020","volume-title":"Forecasting Economic Time Series","author":"Granger","year":"1977"},{"key":"S0266466600007520_ref006","doi-asserted-by":"publisher","DOI":"10.1007\/BF00537538"},{"key":"S0266466600007520_ref003","volume-title":"Testing causality between two vectors in multivariate ARMA models","author":"Boudjellaba","year":"1990"},{"key":"S0266466600007520_ref007","volume-title":"Probabilit\u00e9 et Potentiel","author":"Dellacherie","year":"1975"},{"key":"S0266466600007520_ref008","doi-asserted-by":"publisher","DOI":"10.2307\/1911990"},{"key":"S0266466600007520_ref010","doi-asserted-by":"publisher","DOI":"10.2307\/1912602"},{"key":"S0266466600007520_ref011","doi-asserted-by":"publisher","DOI":"10.2307\/1911729"},{"key":"S0266466600007520_ref012","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9892.1985.tb00395.x"},{"key":"S0266466600007520_ref013","first-page":"353","article-title":"Reduction dans les exp\u00e9riences bayesiennes s\u00e9quentielles","volume":"22","author":"Florens","year":"1980","journal-title":"Cahiers du Centre d'Etudes de Recherche Op\u00e9rationnelle"},{"key":"S0266466600007520_ref016","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(83)90012-X"},{"key":"S0266466600007520_ref017","doi-asserted-by":"publisher","DOI":"10.2307\/20075662"},{"key":"S0266466600007520_ref022","first-page":"219","article-title":"Completeness, similar regions and unbiased tests","volume":"15","author":"Lehmann","year":"1955","journal-title":"Sankhya"},{"key":"S0266466600007520_ref021","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1080\/00031305.1975.10479112","article-title":"On the statistical independence of a sufficient statistics: Basu's lemma","volume":"39","author":"Koehn","year":"1975","journal-title":"The American Statistician"},{"key":"S0266466600007520_ref023","first-page":"557","article-title":"A note on conditional independence (with Statistical Applications)","volume":"44","author":"Mouchart","year":"1984","journal-title":"Statistica"},{"key":"S0266466600007520_ref025","first-page":"269","article-title":"Causality in temporal systems","volume":"51","author":"Pierce","year":"1977","journal-title":"Journal of Econometrics"},{"key":"S0266466600007520_ref026","first-page":"540","article-title":"Money. 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