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Identifiability and Whittle Estimation of Periodic ARMA Models

In: Time Series and Wavelet Analysis

Author

Listed:
  • Alessandro J. Q. Sarnaglia

    (Federal University of Espírito Santo, DEST and LECON
    Federal University of Minas Gerais, PGEST)

  • Valdério A. Reisen

    (Federal University of Espírito Santo, PPGEA and PPEco
    Federal University of Minas Gerais, PGEST
    Laboratoire des signaux et systèmes, PGMAT, Federal University of Bahia and Université Paris-Saclay, CNRS, CentraleSupélec)

  • Pascal Bondon

    (Université Paris-Saclay, CNRS, CentraleSupélec, Laboratoire des signaux et systèmes)

  • Carlo C. Solci

    (PPGEA, Federal University of Espírito Santo)

  • Márton Ispány

    (University of Debrecen)

Abstract

The Periodic Autoregressive Moving Average (PARMA) models are generally assumed to be identifiable. However, this assumption becomes not true if some model conditions are not specified. This paper fills this gap by providing verifiable conditions for the identifiability of PARMA models and, in addition, the Whittle likelihood estimator (WLE) is proposed to estimate the model parameters. This estimator is strongly consistent and asymptotically normal. The Monte Carlo simulation investigation shows that the WLE is a very attractive alternative to the Gaussian maximum likelihood estimator (MLE) for large data sets. Although the estimators have similar accuracy, the computational cost of the MLE is much higher. The methods are applied to fit a PARMA model to the sulfur dioxide (SO 2 $${ }_{2}$$ ) daily average pollutant concentrations measured in the city of Vitória (ES), Brazil.

Suggested Citation

  • Alessandro J. Q. Sarnaglia & Valdério A. Reisen & Pascal Bondon & Carlo C. Solci & Márton Ispány, 2024. "Identifiability and Whittle Estimation of Periodic ARMA Models," Springer Books, in: Chang Chiann & Aluisio de Souza Pinheiro & Clélia Maria Castro Toloi (ed.), Time Series and Wavelet Analysis, pages 149-173, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-66398-7_8
    DOI: 10.1007/978-3-031-66398-7_8
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