A Symbolic Algorithm for Checking the Identifiability of a Time-Series Model
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 n...
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2024-12-01
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| author | Guy Mélard |
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| description | 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 Söderström 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. |
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| institution | Kabale University |
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| language | English |
| publishDate | 2024-12-01 |
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| spelling | doaj-art-d03452922896447c958bde663635db5e2025-01-24T13:35:09ZengMDPI AGInformation2078-24892024-12-011611610.3390/info16010016A Symbolic Algorithm for Checking the Identifiability of a Time-Series ModelGuy Mélard 0Université libre de Bruxelles, Solvay Brussels School of Economics and Management and ECARES, CP 114/04, Avenue Franklin Roosevelt, 50, B-1050 Brussels, BelgiumSeveral 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 Söderström 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.https://www.mdpi.com/2078-2489/16/1/16ARMA modelsVARMA modelsVARMAX modelsWolfram MathematicaGNU MaximaGNU Octave |
| spellingShingle | Guy Mélard A Symbolic Algorithm for Checking the Identifiability of a Time-Series Model Information ARMA models VARMA models VARMAX models Wolfram Mathematica GNU Maxima GNU Octave |
| title | A Symbolic Algorithm for Checking the Identifiability of a Time-Series Model |
| title_full | A Symbolic Algorithm for Checking the Identifiability of a Time-Series Model |
| title_fullStr | A Symbolic Algorithm for Checking the Identifiability of a Time-Series Model |
| title_full_unstemmed | A Symbolic Algorithm for Checking the Identifiability of a Time-Series Model |
| title_short | A Symbolic Algorithm for Checking the Identifiability of a Time-Series Model |
| title_sort | symbolic algorithm for checking the identifiability of a time series model |
| topic | ARMA models VARMA models VARMAX models Wolfram Mathematica GNU Maxima GNU Octave |
| url | https://www.mdpi.com/2078-2489/16/1/16 |
| work_keys_str_mv | AT guymelard asymbolicalgorithmforcheckingtheidentifiabilityofatimeseriesmodel AT guymelard symbolicalgorithmforcheckingtheidentifiabilityofatimeseriesmodel |