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VARMA Models with Single- or Mixed-Frequency Data: New Conditions for Extended Yule–Walker Identification

Author

Listed:
  • Celina Pestano-Gabino

    (Department of Applied Economics and Quantitative Methods, Universidad de La Laguna (ULL), 38200 San Cristóbal de La Laguna, Spain)

  • Concepción González-Concepción

    (Department of Applied Economics and Quantitative Methods, Universidad de La Laguna (ULL), 38200 San Cristóbal de La Laguna, Spain)

  • María Candelaria Gil-Fariña

    (Department of Applied Economics and Quantitative Methods, Universidad de La Laguna (ULL), 38200 San Cristóbal de La Laguna, Spain)

Abstract

This paper deals with the identifiability of VARMA models with VAR order greater than or equal to the MA order, in the context of mixed-frequency data (MFD) using extended Yule–Walker equations. The main contribution is that necessary and sufficient conditions for identifiability in the single-frequency data case are expressed in an original way and yield new results in the MFD case. We also provide two counterexamples that answer an open question in this topic about whether certain sufficient conditions are necessary for identifiability. Therefore, this paper expands the set of models that can be identified with MFD using extended Yule–Walker equations. The main idea is that with MFD, some autocovariance blocks are not available from observed variables and, in some cases, the new conditions in this paper can be used to reconstruct all the non-available covariance blocks from available covariance blocks.

Suggested Citation

  • Celina Pestano-Gabino & Concepción González-Concepción & María Candelaria Gil-Fariña, 2024. "VARMA Models with Single- or Mixed-Frequency Data: New Conditions for Extended Yule–Walker Identification," Mathematics, MDPI, vol. 12(2), pages 1-15, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:2:p:244-:d:1317544
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    References listed on IDEAS

    as
    1. Zadrozny, Peter A., 2016. "Extended Yule–Walker identification of VARMA models with single- or mixed-frequency data," Journal of Econometrics, Elsevier, vol. 193(2), pages 438-446.
    2. Boularouk, Y. & Djeddour, K., 2015. "New approximation for ARMA parameters estimate," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 118(C), pages 116-122.
    3. Anderson, Brian D.O. & Deistler, Manfred & Felsenstein, Elisabeth & Koelbl, Lukas, 2016. "The structure of multivariate AR and ARMA systems: Regular and singular systems; the single and the mixed frequency case," Journal of Econometrics, Elsevier, vol. 192(2), pages 366-373.
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