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Then, we define CIMA processes (i.e., processes admitting a continuous time invertible moving average representation), for which canonical representations and sufficient conditions of invertibility are given. We can provide for those CIMA processes parametric characterizations of noncausality relations as well as properties of interest for structural interpretations. In particular, we examine the example of processes solutions of stochastic differential equations, for which we study the links between continuous and discrete time definitions, find conditions to solve the possible problem of aliasing, and set the question of testing continuous time noncausality on a discrete sample of observations. Finally, we illustrate a possible generalization of definitions and characterizations that can be applied to continuous time fractional ARMA processes.<\/jats:p>","DOI":"10.1017\/s0266466600006575","type":"journal-article","created":{"date-parts":[[2009,3,10]],"date-time":"2009-03-10T15:41:30Z","timestamp":1236699690000},"page":"215-256","source":"Crossref","is-referenced-by-count":33,"title":["Noncausality in Continuous Time Models"],"prefix":"10.1017","volume":"12","author":[{"given":"F.","family":"Comte","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"E.","family":"Renault","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2009,2,11]]},"reference":[{"key":"S0266466600006575_ref027","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02691-5"},{"key":"S0266466600006575_ref020","first-page":"77","volume-title":"Rational Expectations Econometrics","author":"Hansen","year":"1991"},{"key":"S0266466600006575_ref038","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02619-9"},{"key":"S0266466600006575_ref017","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9892.1980.tb00297.x"},{"key":"S0266466600006575_ref044","first-page":"141","volume-title":"Theory of Probability and Statistics","volume":"27","author":"Sekretarev","year":"1984"},{"key":"S0266466600006575_ref016","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(88)90045-0"},{"key":"S0266466600006575_ref030","first-page":"237","volume-title":"Rational Expectations Econometrics","author":"Marcet","year":"1991"},{"key":"S0266466600006575_ref026","volume-title":"Exchange Rate Targets and Currency Bonds","author":"Krugman","year":"1992"},{"key":"S0266466600006575_ref014","volume-title":"Series temporelles et modeles dynamiques","author":"Gourieroux","year":"1990"},{"key":"S0266466600006575_ref012","volume-title":"Econometria","author":"Florens","year":"1996"},{"key":"S0266466600006575_ref031","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(90)90100-8"},{"key":"S0266466600006575_ref022","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(89)90056-0"},{"key":"S0266466600006575_ref025","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02514-7"},{"key":"S0266466600006575_ref019","first-page":"219","volume-title":"Rational Expectations Econometrics","author":"Hansen","year":"1991"},{"key":"S0266466600006575_ref006","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1992.10476263"},{"key":"S0266466600006575_ref033","volume-title":"The Fractional Calculus","author":"Oldham","year":"1974"},{"key":"S0266466600006575_ref015","doi-asserted-by":"publisher","DOI":"10.2307\/1912791"},{"key":"S0266466600006575_ref003","first-page":"1146","volume-title":"Handbook of Econometrics","volume":"2","author":"Bergstrom","year":"1984"},{"key":"S0266466600006575_ref004","volume-title":"Continuous Time Econometric Modelling","author":"Bergstrom","year":"1990"},{"key":"S0266466600006575_ref021","doi-asserted-by":"publisher","DOI":"10.2307\/2297980"},{"key":"S0266466600006575_ref029","doi-asserted-by":"publisher","DOI":"10.1137\/1010093"},{"key":"S0266466600006575_ref001","doi-asserted-by":"publisher","DOI":"10.1111\/j.1540-6261.1993.tb04023.x"},{"key":"S0266466600006575_ref005","doi-asserted-by":"publisher","DOI":"10.1086\/260062"},{"key":"S0266466600006575_ref035","doi-asserted-by":"publisher","DOI":"10.2307\/1912651"},{"key":"S0266466600006575_ref034","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(73)90021-3"},{"key":"S0266466600006575_ref008","volume-title":"Journal of Econometrics","author":"Comte","year":"1996"},{"key":"S0266466600006575_ref013","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9892.1983.tb00371.x"},{"key":"S0266466600006575_ref011","unstructured":"Dufour J.M. & Renault E. 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