{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T12:48:28Z","timestamp":1770295708678,"version":"3.49.0"},"reference-count":46,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2024,12,31]],"date-time":"2024-12-31T00:00:00Z","timestamp":1735603200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>Several authors have attempted to compute the asymptotic Fisher information matrix for a univariate or multivariate time-series model to check for its identifiability. This has the form of a contour integral of a matrix of rational functions. A recent paper has proposed a short Wolfram Mathematica notebook for VARMAX models that makes use of symbolic integration. It cannot be used in open-source symbolic computation software like GNU Octave and GNU Maxima. It was based on symbolic integration but the integrand lacked symmetry characteristics in the appearance of polynomial roots smaller or greater than 1 in modulus. A more symmetric form of the integrand is proposed for VARMA models that first allows a simpler approach to symbolic integration. Second, the computation of the integral through Cauchy residues is also possible. Third, an old numerical algorithm by S\u00f6derstr\u00f6m is used symbolically. These three approaches are investigated and compared on a pair of examples, not only for the Wolfram Language in Mathematica but also for GNU Octave and GNU Maxima. As a consequence, there are now sufficient conditions for exact model identifiability with fast procedures.<\/jats:p>","DOI":"10.3390\/info16010016","type":"journal-article","created":{"date-parts":[[2024,12,31]],"date-time":"2024-12-31T10:17:40Z","timestamp":1735640260000},"page":"16","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Symbolic Algorithm for Checking the Identifiability of a Time-Series Model"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9575-4793","authenticated-orcid":false,"given":"Guy","family":"M\u00e9lard\u00a0","sequence":"first","affiliation":[{"name":"Universit\u00e9 libre de Bruxelles, Solvay Brussels School of Economics and Management and ECARES, CP 114\/04, Avenue Franklin Roosevelt, 50, B-1050 Brussels, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,31]]},"reference":[{"key":"ref_1","first-page":"223","article-title":"The identification of vector mixed autoregressive-moving average systems","volume":"56","author":"Hannan","year":"1969","journal-title":"Biometrika"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"751","DOI":"10.2307\/1909577","article-title":"The identification problem for multiple equation systems with moving average errors","volume":"39","author":"Hannan","year":"1971","journal-title":"Econometrica"},{"key":"ref_3","unstructured":"Hannan, E.J., and Deistler, M. 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