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Identification of canonical models for vectors of time series: a subspace approach

Author

Listed:
  • Alfredo Garcia-Hiernaux

    (Universidad Complutense de Madrid)

  • Jose Casals

    (Universidad Complutense de Madrid)

  • Miguel Jerez

    (Universidad Complutense de Madrid)

Abstract

We propose a new method to specify linear models for vectors of time series with some convenient properties. First, it provides a unified modeling approach for single and multiple time series, as the same decisions are required in both cases. Second, it is scalable, meaning that it provides a quick preliminary model, which can be refined in subsequent modeling phases if required. Third, it is optionally automatic, because the specification depends on a few key parameters which can be determined either automatically or by human decision. And last, it is parsimonious, as it allows one to choose and impose a canonical structure by a novel estimation procedure. Several examples with simulated and real data illustrate its application in practice.

Suggested Citation

  • Alfredo Garcia-Hiernaux & Jose Casals & Miguel Jerez, 2024. "Identification of canonical models for vectors of time series: a subspace approach," Statistical Papers, Springer, vol. 65(3), pages 1493-1530, May.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:3:d:10.1007_s00362-023-01451-y
    DOI: 10.1007/s00362-023-01451-y
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    References listed on IDEAS

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    1. Alfredo García-Hiernaux & José Casals & Miguel Jerez, 2012. "Estimating the system order by subspace methods," Computational Statistics, Springer, vol. 27(3), pages 411-425, September.
    2. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
    3. Alfredo García‐Hiernaux, 2011. "Forecasting linear dynamical systems using subspace methods," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(5), pages 462-468, September.
    4. Dietmar Bauer, 2005. "Comparing the CCA Subspace Method to Pseudo Maximum Likelihood Methods in the case of No Exogenous Inputs," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(5), pages 631-668, September.
    5. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
    6. Lutkepohl, Helmut & Poskitt, D S, 1996. "Specification of Echelon-Form VARMA Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 69-79, January.
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    9. Casals, Jose & Sotoca, Sonia & Jerez, Miguel, 1999. "A fast and stable method to compute the likelihood of time invariant state-space models," Economics Letters, Elsevier, vol. 65(3), pages 329-337, December.
    10. George Athanasopoulos & D. Poskitt & Farshid Vahid, 2012. "Two Canonical VARMA Forms: Scalar Component Models Vis-à-Vis the Echelon Form," Econometric Reviews, Taylor & Francis Journals, vol. 31(1), pages 60-83.
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    13. Casals, J. & García-Hiernaux, A. & Jerez, M., 2012. "From general state-space to VARMAX models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(5), pages 924-936.
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